DOI: 10.1007/bf02128236. Lyapunov Characteristic Exponents for smooth dynamical systems and for hamiltonian systems; a method for computing all of them. Part 1: Theory

Lyapunov Characteristic Exponents for smooth dynamical systems and for hamiltonian systems; a method for computing all of them. Part 1: Theory

10.1007/bf02128236

Crossref journal-article

Springer Science and Business Media LLC

Meccanica (297)

Bibliography

Benettin, G., Galgani, L., Giorgilli, A., & Strelcyn, J.-M. (1980). Lyapunov Characteristic Exponents for smooth dynamical systems and for hamiltonian systems; a method for computing all of them. Part 1: Theory. Meccanica, 15(1), 9â20.

Authors 4

Giancarlo Benettin (first)
Luigi Galgani (additional)
Antonio Giorgilli (additional)
Jean-Marie Strelcyn (additional)

References 28 Referenced 1,479

Lyapunov A. M.,Problème Général de la Mouvement (transl. from Russian), Ann. Fac. Sci. Univ. Touluse9, p. 203–475, 1907. Reproduced in Ann. Math. Study, vol. 17, Princeton 1947. (10.5802/afst.246) / Ann. Fac. Sci. Univ. Touluse by A. M. Lyapunov (1907)
Demidovich B. P.,Lectures on Mathematical Theory of Stability (in Russian), ed. Nauka Moscow, 1967.
Bylov B. F., Vinograd R. E., Grobman D. M. andNemyckij V. V.,The Theory of Lyapunov Characteristic Numbers and their Application to the Theory of Stability (in Russian), ed. Nauka Moscow, 1966.
Cesari L.,Asymptotic Behaviour and Stability Problems in Ordinary Differential Equations, Springer-Verlag, Berlin, 1959. / Asymptotic Behaviour and Stability Problems in Ordinary Differential Equations by L. Cesari (1959)
Oseldec V. I.,The Multiplicative Ergodic Theorem. The Lyapunov Characteristic Numbers of Dynamical Systems, (in Russian). Trudy Mosk. Mat. Obsch.19, p. 179–210, 1968. English traslation in Trans. Mosc. Math. Soc.19, p. 197, 1968. / Trudy Mosk. Mat. Obsch. by V. I. Oseldec (1968)
Benettin G., Galgani L. andStrelcyn J.-M.,Kolmogrov Entropy and Numerical Experiments, Phys. Rev.A14, p. 2338–2345, 1976. (10.1103/PhysRevA.14.2338) / Phys. Rev. by G. Benettin (1976)
Contopoulos G., Galgani L. andGiorgilli A.,On the Number of Isolating Integrals for Hamiltonian Systems, Phys. Rev.A18, p. 1183–1189, 1978. (10.1103/PhysRevA.18.1183) / Phys. Rev. by G. Contopoulos (1978)
Chirikov B. V.,Researches Concerning the Theory of Nonlinear Resonances and Stochasticity, CERN Trans. No. 71 - 40 (Geneva, 1971).
Chirikov B. V. andIzrailev F. M.,Nonlinear Mapping: Stochastic Components, in Colloque International CNRS sur les Transformations Ponctuelles et leurs Applications, ed. du CNRS Paris, 1976.
Casartelli M., Diana E., Galgani L. andScotti A.,Numerical Computations on a Stochastic Parameter related to the Kolmogorov Entropy, Phys Rev.A13, p. 1921–1925, 1976. (10.1103/PhysRevA.13.1921) / Phys Rev. by M. Casartelli (1976)
Pesin Ya. B.,Lyapunov Characteristic Exponents and Smooth Ergodic Theory (in Russian), Uspekhi Mat. Nauk.32, N. 4, p. 55–112, 1977; Engl. Transl. in Russ. Math. Surveys,32, N. 4, p. 55 – 114, 1977. / Uspekhi Mat. Nauk. by Ya. B. Pesin (1977)
Benettin G. andStrelcyn J.-M.,Numerical Experiments on the Free Motion of a Point Mass Moving in a Plane Convex Region, Stochastic Transition and Entropy, Phys. Rev.A17, p. 773–785, 1978. (10.1103/PhysRevA.17.773) / Phys. Rev. by G. Benettin (1978)
Benettin G., Galgani L., Giorgilli A. andStrelcyn J.-M.,Tous les Nombres Caractéristiques de Lyapounov sont effectivement calculables, C.R. Acad. Sc. Paris, 286A, p. 431–433, 1978. / C.R. Acad. Sc. Paris by G. Benettin (1978)
Benettin G., Froeschle C. andScheidecker J. P.,Kolmogorov Entropy of a Dynamical System with Increasing Number of Degrees of Freedom, Phys. Rev.A19, p. 2454–2460, 1979. (10.1103/PhysRevA.19.2454) / Phys. Rev. by G. Benettin (1979)
Benettin G., Galgani L., Giorgilli A. andStrelcyn J.-M.,Lyapunov Characteristic Exponents for Smooth Dynamical Systems and for Hamiltonian Systems; a Method for Computing all of them, Part II: Numerical Application, Meccanica.
Ruelle D.,Analiticity Properties of the Characteristic Exponents of Random Matrix Products, IHES preprint 1977.
Raghunathan M. S.,A Proof of the Oseledec Multiplicative Ergodic Theorem, (to be published).
Shilov G. E.,Introduction to be the Theory of Linear Spaces, Dover Publ, New York 1961.
Ruelle D.,Ergodic Theory of Differentiable Dynamical Systems, IHES preprint 1978.
Walters P.,Ergodic Theory; Introductory Lectures, Notes in Mathematics No. 458, Springer-Verlag, Berlin, 1975. (10.1007/BFb0112501) / Ergodic Theory; Introductory Lectures / Notes in Mathematics by P. Walters (1975)
Ruelle D.,Sensitive Dependence on Initial Condition and Turbulent Behaviour of Dynamical Systems, Lect. Notes in Phys. No. 80, Springer-Verlag, Berlin, 1978. / Sensitive Dependence on Initial Condition and Turbulent Behaviour of Dynamical Systems / Lect. Notes in Phys. by D. Ruelle (1978)
Sternberg S.,Lectures on Differential Geometry, Prentice Hall, Engl. Cl., N. J., 1966.
Shilov G. E. andGurevich B. L.,Integral, Measure and Derivative: A unified Approach, Prentice Hall, Engl. Cl., N. J., 1966. Reprinted by Dover Publ. New York 1974.
Arnold V. I.,Mathematical Methods of Classical Mechanics, Springer-Verlag, Berlin, 1978. (10.1007/978-1-4757-1693-1) / Mathematical Methods of Classical Mechanics by V. I. Arnold (1978)
Kac M.,Probability and Related Topics in Physical Sciences, Interscience, London, 1959. / Probability and Related Topics in Physical Sciences by M. Kac (1959)
Perron O.,Die Stabilitätsfrage bei Differentialgleichungen, Math. Zeit.32, p. 703–728, 1930. (10.1007/BF01194662) / Math. Zeit. by O. Perron (1930)
Halmos P. R.,Lectures on Ergodic Theory, Publ. of the Math. Soc. of Japan, Tokyo, 1956. Reprinted by Chelsea Publ. Comp. N. Y., 1960.
Rochlin V. A.,Selected Topics from the Metric Theory of Dynamical Systems (in Russian), Uspekhi Mat. Nauk.4, 2, p. 57–128 1949. English Transl. in Amer. Math. Soc. Trans.49, p. 171 – 240 1965. / Uspekhi Mat. Nauk. by V. A. Rochlin (1949)

Dates

Type	When
Created	19 years, 11 months ago (Sept. 14, 2005, 6:58 a.m.)
Deposited	6 years, 3 months ago (May 13, 2019, 5:45 p.m.)
Indexed	20 hours, 53 minutes ago (Aug. 27, 2025, 11:53 a.m.)
Issued	45 years, 5 months ago (March 1, 1980)
Published	45 years, 5 months ago (March 1, 1980)
Published Print	45 years, 5 months ago (March 1, 1980)

Funders 0

None

BibTeX

@article{Benettin_1980, title={Lyapunov Characteristic Exponents for smooth dynamical systems and for hamiltonian systems; a method for computing all of them. Part 1: Theory}, volume={15}, ISSN={1572-9648}, url={http://dx.doi.org/10.1007/bf02128236}, DOI={10.1007/bf02128236}, number={1}, journal={Meccanica}, publisher={Springer Science and Business Media LLC}, author={Benettin, Giancarlo and Galgani, Luigi and Giorgilli, Antonio and Strelcyn, Jean-Marie}, year={1980}, month=mar, pages={9–20} }

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