DOI: 10.1007/bf01258529. Characteristic exponents for a viscous fluid subjected to time dependent forces

Characteristic exponents for a viscous fluid subjected to time dependent forces

10.1007/bf01258529

Crossref journal-article

Springer Science and Business Media LLC

Communications in Mathematical Physics (297)

Bibliography

Ruelle, D. (1984). Characteristic exponents for a viscous fluid subjected to time dependent forces. Communications in Mathematical Physics, 93(3), 285â300.

Authors 1

David Ruelle (first)

References 37 Referenced 88

Bourbaki, N.: Elements de Mathématiques, Livre VI. Intégration. Chap. 6. Intégration vectorielle, A.S.I. 1281, Paris: Herman 1959 / Elements de Mathématiques, Livre VI. Intégration. Chap. 6. Intégration vectorielle, A.S.I. 1281 by N. Bourbaki (1959)
Caffarelli, L., Kohn, R., Nirenberg, L.: Partial regularity of suitable weak solutions of the Navier-Stokes equations. Commun. Pure Appl. Math.35, 771?831 (1982) (10.1002/cpa.3160350604) / Commun. Pure Appl. Math. by L. Caffarelli (1982)
Chandrasekhar, S.: Hydrodynamic and hydromagnetic stability. Oxford: Clarendon 1961 / Hydrodynamic and hydromagnetic stability by S. Chandrasekhar (1961)
Constantin, P., Foias, C.: Global Lyapunov exponents, Kaplan-Yorke formulas and the dimension of the attractors for 2D Navier-Stokes equations. (to appear)
Constantin, P., Foias, C., Manley, O., Temam, R.: Analyse mathématique et mécanique des fluides ? connection entre la théorie mathématique des équations de Navier-Stokes et la théorie conventionnelle de la turbulence. CRAS Paris (to appear)
Douady, A., Oesterlé, J.: Dimension de Hausdorff des attracteurs. C.R. Acad. Sci. Paris290 A, 1135?1138 (1980) / C.R. Acad. Sci. Paris by A. Douady (1980)
Fefferman, C.: The uncertainty principle. Bull. Am. Math. Soc.9, 129?206 (1983) (10.1090/S0273-0979-1983-15154-6) / Bull. Am. Math. Soc. by C. Fefferman (1983)
Foias, C., Temam, R.: Some analytic and geometric properties of the solutions of the evolution Navier-Stokes equations. J. Math. Pures Appl.58, 339?368 (1979) / J. Math. Pures Appl. by C. Foias (1979)
Frederikson, P., Kaplan, J.L., Yorke, J.A.: The dimension of the strange attractor for a class of difference systems. Preprint
Furstenberg, H., Kesten, H.: Products of random matrices. Ann. Math. Stat.31, 457?469 (1960) (10.1214/aoms/1177705909) / Ann. Math. Stat. by H. Furstenberg (1960)
Glansdorff, P., Prigogine, I.: Structure, stabilité et fluctuations. Paris: Masson 1971 / Structure, stabilité et fluctuations by P. Glansdorff (1971)
Grassberger, P., Procaccia, I.: Characterization of strange attractors. Phys. Rev. Lett.50, 346?349 (1983) (10.1103/PhysRevLett.50.346) / Phys. Rev. Lett. by P. Grassberger (1983)
Hopf, E.: Über die Anfangswertaufgabe für die hydrodynamischen Grundgleichungen. Math. Nachrichten4, 213?331 (1951) (10.1002/mana.3210040121) / Math. Nachrichten by E. Hopf (1951)
Jacobs, K.: Lecture notes on ergodic theory. Aarhus Universitet, Aarhus, 1963
Ladyzhenskaya, O.A.: The mathematical theory of viscous incompressible flow (2nd edn.), Moscow: Nauka, 1970, 2nd English edn. New York: Gordon and Breach 1969 / The mathematical theory of viscous incompressible flow by O.A. Ladyzhenskaya (1970)
Ledrappier, F.: Some relations between dimension and Lyapounov exponents. Commun. Math. Phys.81, 229?238 (1981) (10.1007/BF01208896) / Commun. Math. Phys. by F. Ledrappier (1981)
Leray, J.: Sur le mouvement d'un liquide visqueux emplissant l'espace. Acta Math.63, 193?248 (1934) (10.1007/BF02547354) / Acta Math. by J. Leray (1934)
Lieb, E.: On characteristic exponents in turbulence. Commun. Math. Phys.92, 473?480 (1984) (10.1007/BF01215277) / Commun. Math. Phys. by E. Lieb (1984)
Lieb, E., Thirring, W.: Inequalities for the moments of the eigenvalues of the Schrödinger equation and their relation to Sobolev inequalities, pp. 269?303. In: Studies in Mathematical Physics: Essays in Honor of Valentine Bargman. Lieb, E., Simon, B., Wightman, A.S. (eds.), Princeton, N.J.: Princeton University Press 1976 / Studies in Mathematical Physics: Essays in Honor of Valentine Bargman by E. Lieb (1976)
Lions, J.L.: Quelques méthodes de résolution des problèmes aux limites non-linéaires, Paris: Dunod 1969 / Quelques méthodes de résolution des problèmes aux limites non-linéaires by J.L. Lions (1969)
Mallet-Paret, J.: Negatively invariant sets of compact maps and an extension of a theorem of Cartwright. J. Diff. Eq.22, 331?348 (1976) (10.1016/0022-0396(76)90032-2) / J. Diff. Eq. by J. Mallet-Paret (1976)
Malraison, B., Atten, P., Bergé, P., Dubois, M.: Dimension of strange attractors: an experimental determination for the chaotic regime of two convective systems. J. Phys. Lett.44, L-897?902 (1983) (10.1051/jphyslet:019830044022089700) / J. Phys. Lett. by B. Malraison (1983)
Mañè, R.: On the dimension of the compact invariant sets of certain nonlinear maps, pp. 230?242. In: Dynamical systems and turbulence, Warwick 1980, Lecture Notes in Mathematics, Vol.898, New York: Springer 1981 (10.1007/BFb0091916) / Dynamical systems and turbulence, Warwick 1980 / Lecture Notes in Mathematics by R. Mañè (1981)
Mañé, R.: Lyapounov exponents and stable manifolds for compact transformations, pp. 522?577. In: Geometric dynamics. Lecture Notes in Mathematics, Vol. 1007, Berlin, Heidelberg, New York: Springer 1983 (10.1007/BFb0061433) / Geometric dynamics / Lecture Notes in Mathematics by R. Mañé (1983)
McCluskey, H., Manning, A.: Hausdorff dimension for horseshoes, Ergod. Th. and Dynam. Syst.3, 251?260 (1983) (10.1017/S0143385700001966) / Ergod. Th. and Dynam. Syst. by H. McCluskey (1983)
Oseledec, V.I.: A multiplicative ergodic theorem. Lyapunov characteristic numbers for dynamical systems. Tr. Mosk. Mat. Ob??.19, 179?210 (1968), English translation, Trans. Moscow Math. Soc.19, 197?221 (1968) / Tr. Mosk. Mat. Ob??. by V.I. Oseledec (1968)
Raghunathan, M.S.: A proof of Oseledec' multiplicative ergodic theorem. Israel J. Math.32, 356?362 (1979) (10.1007/BF02760464) / Israel J. Math. by M.S. Raghunathan (1979)
Reed, M., Simon, B.: Methods of modern mathematical physics. New York: Academic Press 1972 (I), 1975 (II), 1979 (III), 1978 (IV) / Methods of modern mathematical physics by M. Reed (1972)
Ruelle, D.: An inequality for the entropy of differentiable maps. Bol. Soc. Bras. Mat.9, 83?87 (1978) (10.1007/BF02584795) / Bol. Soc. Bras. Mat. by D. Ruelle (1978)
Ruelle, D.: Ergodic theory of differentiable dynamical systems. Publ. Math. IHES50, 275?306 (1979) (10.1007/BF02684768) / Publ. Math. IHES by D. Ruelle (1979)
Ruelle, D.: Characteristic exponents and invariant manifolds in Hilbert space. Ann. Math.115, 243?290 (1982) (10.2307/1971392) / Ann. Math. by D. Ruelle (1982)
Ruelle, D.: Large volume limit of the distribution of characteristic exponents in turbulence. Commun. Math. Phys.87, 287?302 (1982) (10.1007/BF01218566) / Commun. Math. Phys. by D. Ruelle (1982)
Scheffer, V.: Turbulence and Hausdorff dimension, pp. 174?183. In: Turbulence and Navier-Stokes equation, Lecture Notes in Mathematics, Vol.565, Berlin: Springer 1976 (10.1007/BFb0091455) / Turbulence and Navier-Stokes equation / Lecture Notes in Mathematics by V. Scheffer (1976)
Scheffer, V.: The Navier-Stokes equations on a bounded domain. Commun. Math. Phys.73, 1?42 (1980) (10.1007/BF01942692) / Commun. Math. Phys. by V. Scheffer (1980)
Tartar, L.: Topics in nonlinear analysis. Publications mathématiques d'Orsay 78.13, Orsay, 1978
Temam, R.: Navier-Stokes equations. Revised edition, Amsterdam: North-Holland 1979 / Navier-Stokes equations by R. Temam (1979)
Young, L.-S.: Dimension, entropy and Lyapounov exponents. Ergod. Theor. Dynam. Syst.2, 109?124 (1982) (10.1017/S0143385700009615) / Ergod. Theor. Dynam. Syst. by L.-S. Young (1982)

Dates

Type	When
Created	20 years, 5 months ago (March 23, 2005, 6:23 p.m.)
Deposited	6 years, 3 months ago (May 2, 2019, 7:01 a.m.)
Indexed	3 weeks ago (Aug. 6, 2025, 8:07 a.m.)
Issued	40 years, 11 months ago (Sept. 1, 1984)
Published	40 years, 11 months ago (Sept. 1, 1984)
Published Print	40 years, 11 months ago (Sept. 1, 1984)

Funders 0

None

BibTeX

@article{Ruelle_1984, title={Characteristic exponents for a viscous fluid subjected to time dependent forces}, volume={93}, ISSN={1432-0916}, url={http://dx.doi.org/10.1007/bf01258529}, DOI={10.1007/bf01258529}, number={3}, journal={Communications in Mathematical Physics}, publisher={Springer Science and Business Media LLC}, author={Ruelle, David}, year={1984}, month=sep, pages={285–300} }

JSON

{
  "indexed": {
    "date-parts": [
      [
        2025,
        8,
        6
      ]
    ],
    "date-time": "2025-08-06T12:07:21Z",
    "timestamp": 1754482041416
  },
  "reference-count": 37,
  "publisher": "Springer Science and Business Media LLC",
  "issue": "3",
  "license": [
    {
      "start": {
        "date-parts": [
          [
            1984,
            9,
            1
          ]
        ],
        "date-time": "1984-09-01T00:00:00Z",
        "timestamp": 462844800000
      },
      "content-version": "tdm",
      "delay-in-days": 0,
      "URL": "http://www.springer.com/tdm"
    }
  ],
  "content-domain": {
    "domain": [],
    "crossmark-restriction": false
  },
  "published-print": {
    "date-parts": [
      [
        1984,
        9
      ]
    ]
  },
  "DOI": "10.1007/bf01258529",
  "type": "journal-article",
  "created": {
    "date-parts": [
      [
        2005,
        3,
        23
      ]
    ],
    "date-time": "2005-03-23T23:23:14Z",
    "timestamp": 1111620194000
  },
  "page": "285-300",
  "source": "Crossref",
  "is-referenced-by-count": 88,
  "title": "Characteristic exponents for a viscous fluid subjected to time dependent forces",
  "prefix": "10.1007",
  "volume": "93",
  "author": [
    {
      "given": "David",
      "family": "Ruelle",
      "sequence": "first",
      "affiliation": []
    }
  ],
  "member": "297",
  "reference": [
    {
      "key": "CR1",
      "volume-title": "Elements de Math\u00e9matiques, Livre VI. Int\u00e9gration. Chap. 6. Int\u00e9gration vectorielle, A.S.I. 1281",
      "author": "N. Bourbaki",
      "year": "1959",
      "unstructured": "Bourbaki, N.: Elements de Math\u00e9matiques, Livre VI. Int\u00e9gration. Chap. 6. Int\u00e9gration vectorielle, A.S.I. 1281, Paris: Herman 1959"
    },
    {
      "key": "CR2",
      "doi-asserted-by": "crossref",
      "first-page": "771",
      "DOI": "10.1002/cpa.3160350604",
      "volume": "35",
      "author": "L. Caffarelli",
      "year": "1982",
      "unstructured": "Caffarelli, L., Kohn, R., Nirenberg, L.: Partial regularity of suitable weak solutions of the Navier-Stokes equations. Commun. Pure Appl. Math.35, 771?831 (1982)",
      "journal-title": "Commun. Pure Appl. Math."
    },
    {
      "key": "CR3",
      "volume-title": "Hydrodynamic and hydromagnetic stability",
      "author": "S. Chandrasekhar",
      "year": "1961",
      "unstructured": "Chandrasekhar, S.: Hydrodynamic and hydromagnetic stability. Oxford: Clarendon 1961"
    },
    {
      "key": "CR4",
      "unstructured": "Constantin, P., Foias, C.: Global Lyapunov exponents, Kaplan-Yorke formulas and the dimension of the attractors for 2D Navier-Stokes equations. (to appear)"
    },
    {
      "key": "CR5",
      "unstructured": "Constantin, P., Foias, C., Manley, O., Temam, R.: Analyse math\u00e9matique et m\u00e9canique des fluides ? connection entre la th\u00e9orie math\u00e9matique des \u00e9quations de Navier-Stokes et la th\u00e9orie conventionnelle de la turbulence. CRAS Paris (to appear)"
    },
    {
      "key": "CR6",
      "first-page": "1135",
      "volume": "290",
      "author": "A. Douady",
      "year": "1980",
      "unstructured": "Douady, A., Oesterl\u00e9, J.: Dimension de Hausdorff des attracteurs. C.R. Acad. Sci. Paris290 A, 1135?1138 (1980)",
      "journal-title": "C.R. Acad. Sci. Paris"
    },
    {
      "key": "CR7",
      "doi-asserted-by": "crossref",
      "first-page": "129",
      "DOI": "10.1090/S0273-0979-1983-15154-6",
      "volume": "9",
      "author": "C. Fefferman",
      "year": "1983",
      "unstructured": "Fefferman, C.: The uncertainty principle. Bull. Am. Math. Soc.9, 129?206 (1983)",
      "journal-title": "Bull. Am. Math. Soc."
    },
    {
      "key": "CR8",
      "first-page": "339",
      "volume": "58",
      "author": "C. Foias",
      "year": "1979",
      "unstructured": "Foias, C., Temam, R.: Some analytic and geometric properties of the solutions of the evolution Navier-Stokes equations. J. Math. Pures Appl.58, 339?368 (1979)",
      "journal-title": "J. Math. Pures Appl."
    },
    {
      "key": "CR9",
      "unstructured": "Frederikson, P., Kaplan, J.L., Yorke, J.A.: The dimension of the strange attractor for a class of difference systems. Preprint"
    },
    {
      "key": "CR10",
      "doi-asserted-by": "crossref",
      "first-page": "457",
      "DOI": "10.1214/aoms/1177705909",
      "volume": "31",
      "author": "H. Furstenberg",
      "year": "1960",
      "unstructured": "Furstenberg, H., Kesten, H.: Products of random matrices. Ann. Math. Stat.31, 457?469 (1960)",
      "journal-title": "Ann. Math. Stat."
    },
    {
      "key": "CR11",
      "volume-title": "Structure, stabilit\u00e9 et fluctuations",
      "author": "P. Glansdorff",
      "year": "1971",
      "unstructured": "Glansdorff, P., Prigogine, I.: Structure, stabilit\u00e9 et fluctuations. Paris: Masson 1971"
    },
    {
      "key": "CR12",
      "doi-asserted-by": "crossref",
      "first-page": "346",
      "DOI": "10.1103/PhysRevLett.50.346",
      "volume": "50",
      "author": "P. Grassberger",
      "year": "1983",
      "unstructured": "Grassberger, P., Procaccia, I.: Characterization of strange attractors. Phys. Rev. Lett.50, 346?349 (1983)",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "CR13",
      "doi-asserted-by": "crossref",
      "first-page": "213",
      "DOI": "10.1002/mana.3210040121",
      "volume": "4",
      "author": "E. Hopf",
      "year": "1951",
      "unstructured": "Hopf, E.: \u00dcber die Anfangswertaufgabe f\u00fcr die hydrodynamischen Grundgleichungen. Math. Nachrichten4, 213?331 (1951)",
      "journal-title": "Math. Nachrichten"
    },
    {
      "key": "CR14",
      "unstructured": "Jacobs, K.: Lecture notes on ergodic theory. Aarhus Universitet, Aarhus, 1963"
    },
    {
      "key": "CR15",
      "volume-title": "The mathematical theory of viscous incompressible flow",
      "author": "O.A. Ladyzhenskaya",
      "year": "1970",
      "unstructured": "Ladyzhenskaya, O.A.: The mathematical theory of viscous incompressible flow (2nd edn.), Moscow: Nauka, 1970, 2nd English edn. New York: Gordon and Breach 1969",
      "edition": "2nd edn."
    },
    {
      "key": "CR16",
      "doi-asserted-by": "crossref",
      "first-page": "229",
      "DOI": "10.1007/BF01208896",
      "volume": "81",
      "author": "F. Ledrappier",
      "year": "1981",
      "unstructured": "Ledrappier, F.: Some relations between dimension and Lyapounov exponents. Commun. Math. Phys.81, 229?238 (1981)",
      "journal-title": "Commun. Math. Phys."
    },
    {
      "key": "CR17",
      "doi-asserted-by": "crossref",
      "first-page": "193",
      "DOI": "10.1007/BF02547354",
      "volume": "63",
      "author": "J. Leray",
      "year": "1934",
      "unstructured": "Leray, J.: Sur le mouvement d'un liquide visqueux emplissant l'espace. Acta Math.63, 193?248 (1934)",
      "journal-title": "Acta Math."
    },
    {
      "key": "CR18",
      "doi-asserted-by": "crossref",
      "first-page": "473",
      "DOI": "10.1007/BF01215277",
      "volume": "92",
      "author": "E. Lieb",
      "year": "1984",
      "unstructured": "Lieb, E.: On characteristic exponents in turbulence. Commun. Math. Phys.92, 473?480 (1984)",
      "journal-title": "Commun. Math. Phys."
    },
    {
      "key": "CR19",
      "first-page": "269",
      "volume-title": "Studies in Mathematical Physics: Essays in Honor of Valentine Bargman",
      "author": "E. Lieb",
      "year": "1976",
      "unstructured": "Lieb, E., Thirring, W.: Inequalities for the moments of the eigenvalues of the Schr\u00f6dinger equation and their relation to Sobolev inequalities, pp. 269?303. In: Studies in Mathematical Physics: Essays in Honor of Valentine Bargman. Lieb, E., Simon, B., Wightman, A.S. (eds.), Princeton, N.J.: Princeton University Press 1976"
    },
    {
      "key": "CR20",
      "volume-title": "Quelques m\u00e9thodes de r\u00e9solution des probl\u00e8mes aux limites non-lin\u00e9aires",
      "author": "J.L. Lions",
      "year": "1969",
      "unstructured": "Lions, J.L.: Quelques m\u00e9thodes de r\u00e9solution des probl\u00e8mes aux limites non-lin\u00e9aires, Paris: Dunod 1969"
    },
    {
      "key": "CR21",
      "doi-asserted-by": "crossref",
      "first-page": "331",
      "DOI": "10.1016/0022-0396(76)90032-2",
      "volume": "22",
      "author": "J. Mallet-Paret",
      "year": "1976",
      "unstructured": "Mallet-Paret, J.: Negatively invariant sets of compact maps and an extension of a theorem of Cartwright. J. Diff. Eq.22, 331?348 (1976)",
      "journal-title": "J. Diff. Eq."
    },
    {
      "key": "CR22",
      "doi-asserted-by": "crossref",
      "first-page": "L-897",
      "DOI": "10.1051/jphyslet:019830044022089700",
      "volume": "44",
      "author": "B. Malraison",
      "year": "1983",
      "unstructured": "Malraison, B., Atten, P., Berg\u00e9, P., Dubois, M.: Dimension of strange attractors: an experimental determination for the chaotic regime of two convective systems. J. Phys. Lett.44, L-897?902 (1983)",
      "journal-title": "J. Phys. Lett."
    },
    {
      "key": "CR23",
      "series-title": "Lecture Notes in Mathematics",
      "doi-asserted-by": "crossref",
      "first-page": "230",
      "DOI": "10.1007/BFb0091916",
      "volume-title": "Dynamical systems and turbulence, Warwick 1980",
      "author": "R. Ma\u00f1\u00e8",
      "year": "1981",
      "unstructured": "Ma\u00f1\u00e8, R.: On the dimension of the compact invariant sets of certain nonlinear maps, pp. 230?242. In: Dynamical systems and turbulence, Warwick 1980, Lecture Notes in Mathematics, Vol.898, New York: Springer 1981"
    },
    {
      "key": "CR24",
      "series-title": "Lecture Notes in Mathematics",
      "doi-asserted-by": "crossref",
      "first-page": "522",
      "DOI": "10.1007/BFb0061433",
      "volume-title": "Geometric dynamics",
      "author": "R. Ma\u00f1\u00e9",
      "year": "1983",
      "unstructured": "Ma\u00f1\u00e9, R.: Lyapounov exponents and stable manifolds for compact transformations, pp. 522?577. In: Geometric dynamics. Lecture Notes in Mathematics, Vol. 1007, Berlin, Heidelberg, New York: Springer 1983"
    },
    {
      "key": "CR25",
      "doi-asserted-by": "crossref",
      "first-page": "251",
      "DOI": "10.1017/S0143385700001966",
      "volume": "3",
      "author": "H. McCluskey",
      "year": "1983",
      "unstructured": "McCluskey, H., Manning, A.: Hausdorff dimension for horseshoes, Ergod. Th. and Dynam. Syst.3, 251?260 (1983)",
      "journal-title": "Ergod. Th. and Dynam. Syst."
    },
    {
      "key": "CR26",
      "first-page": "179",
      "volume": "19",
      "author": "V.I. Oseledec",
      "year": "1968",
      "unstructured": "Oseledec, V.I.: A multiplicative ergodic theorem. Lyapunov characteristic numbers for dynamical systems. Tr. Mosk. Mat. Ob??.19, 179?210 (1968), English translation, Trans. Moscow Math. Soc.19, 197?221 (1968)",
      "journal-title": "Tr. Mosk. Mat. Ob??."
    },
    {
      "key": "CR27",
      "doi-asserted-by": "crossref",
      "first-page": "356",
      "DOI": "10.1007/BF02760464",
      "volume": "32",
      "author": "M.S. Raghunathan",
      "year": "1979",
      "unstructured": "Raghunathan, M.S.: A proof of Oseledec' multiplicative ergodic theorem. Israel J. Math.32, 356?362 (1979)",
      "journal-title": "Israel J. Math."
    },
    {
      "key": "CR28",
      "volume-title": "Methods of modern mathematical physics",
      "author": "M. Reed",
      "year": "1972",
      "unstructured": "Reed, M., Simon, B.: Methods of modern mathematical physics. New York: Academic Press 1972 (I), 1975 (II), 1979 (III), 1978 (IV)"
    },
    {
      "key": "CR29",
      "doi-asserted-by": "crossref",
      "first-page": "83",
      "DOI": "10.1007/BF02584795",
      "volume": "9",
      "author": "D. Ruelle",
      "year": "1978",
      "unstructured": "Ruelle, D.: An inequality for the entropy of differentiable maps. Bol. Soc. Bras. Mat.9, 83?87 (1978)",
      "journal-title": "Bol. Soc. Bras. Mat."
    },
    {
      "key": "CR30",
      "doi-asserted-by": "crossref",
      "first-page": "275",
      "DOI": "10.1007/BF02684768",
      "volume": "50",
      "author": "D. Ruelle",
      "year": "1979",
      "unstructured": "Ruelle, D.: Ergodic theory of differentiable dynamical systems. Publ. Math. IHES50, 275?306 (1979)",
      "journal-title": "Publ. Math. IHES"
    },
    {
      "key": "CR31",
      "doi-asserted-by": "crossref",
      "first-page": "243",
      "DOI": "10.2307/1971392",
      "volume": "115",
      "author": "D. Ruelle",
      "year": "1982",
      "unstructured": "Ruelle, D.: Characteristic exponents and invariant manifolds in Hilbert space. Ann. Math.115, 243?290 (1982)",
      "journal-title": "Ann. Math."
    },
    {
      "key": "CR32",
      "doi-asserted-by": "crossref",
      "first-page": "287",
      "DOI": "10.1007/BF01218566",
      "volume": "87",
      "author": "D. Ruelle",
      "year": "1982",
      "unstructured": "Ruelle, D.: Large volume limit of the distribution of characteristic exponents in turbulence. Commun. Math. Phys.87, 287?302 (1982)",
      "journal-title": "Commun. Math. Phys."
    },
    {
      "key": "CR33",
      "series-title": "Lecture Notes in Mathematics",
      "doi-asserted-by": "crossref",
      "first-page": "174",
      "DOI": "10.1007/BFb0091455",
      "volume-title": "Turbulence and Navier-Stokes equation",
      "author": "V. Scheffer",
      "year": "1976",
      "unstructured": "Scheffer, V.: Turbulence and Hausdorff dimension, pp. 174?183. In: Turbulence and Navier-Stokes equation, Lecture Notes in Mathematics, Vol.565, Berlin: Springer 1976"
    },
    {
      "key": "CR34",
      "doi-asserted-by": "crossref",
      "first-page": "1",
      "DOI": "10.1007/BF01942692",
      "volume": "73",
      "author": "V. Scheffer",
      "year": "1980",
      "unstructured": "Scheffer, V.: The Navier-Stokes equations on a bounded domain. Commun. Math. Phys.73, 1?42 (1980)",
      "journal-title": "Commun. Math. Phys."
    },
    {
      "key": "CR35",
      "unstructured": "Tartar, L.: Topics in nonlinear analysis. Publications math\u00e9matiques d'Orsay 78.13, Orsay, 1978"
    },
    {
      "key": "CR36",
      "volume-title": "Navier-Stokes equations",
      "author": "R. Temam",
      "year": "1979",
      "unstructured": "Temam, R.: Navier-Stokes equations. Revised edition, Amsterdam: North-Holland 1979",
      "edition": "Revised edition"
    },
    {
      "key": "CR37",
      "doi-asserted-by": "crossref",
      "first-page": "109",
      "DOI": "10.1017/S0143385700009615",
      "volume": "2",
      "author": "L.-S. Young",
      "year": "1982",
      "unstructured": "Young, L.-S.: Dimension, entropy and Lyapounov exponents. Ergod. Theor. Dynam. Syst.2, 109?124 (1982)",
      "journal-title": "Ergod. Theor. Dynam. Syst."
    }
  ],
  "container-title": "Communications in Mathematical Physics",
  "original-title": [],
  "language": "en",
  "link": [
    {
      "URL": "http://link.springer.com/content/pdf/10.1007/BF01258529.pdf",
      "content-type": "application/pdf",
      "content-version": "vor",
      "intended-application": "text-mining"
    },
    {
      "URL": "http://link.springer.com/article/10.1007/BF01258529/fulltext.html",
      "content-type": "text/html",
      "content-version": "vor",
      "intended-application": "text-mining"
    },
    {
      "URL": "http://link.springer.com/content/pdf/10.1007/BF01258529",
      "content-type": "unspecified",
      "content-version": "vor",
      "intended-application": "similarity-checking"
    }
  ],
  "deposited": {
    "date-parts": [
      [
        2019,
        5,
        2
      ]
    ],
    "date-time": "2019-05-02T11:01:52Z",
    "timestamp": 1556794912000
  },
  "score": 1,
  "resource": {
    "primary": {
      "URL": "http://link.springer.com/10.1007/BF01258529"
    }
  },
  "subtitle": [],
  "short-title": [],
  "issued": {
    "date-parts": [
      [
        1984,
        9
      ]
    ]
  },
  "references-count": 37,
  "journal-issue": {
    "issue": "3",
    "published-print": {
      "date-parts": [
        [
          1984,
          9
        ]
      ]
    }
  },
  "alternative-id": [
    "BF01258529"
  ],
  "URL": "http://dx.doi.org/10.1007/BF01258529",
  "relation": {},
  "ISSN": [
    "0010-3616",
    "1432-0916"
  ],
  "subject": [],
  "container-title-short": "Commun.Math. Phys.",
  "published": {
    "date-parts": [
      [
        1984,
        9
      ]
    ]
  }
}