DOI: 10.1007/bf01049033. Ergodic properties of the discontinuous sawtooth map

Ergodic properties of the discontinuous sawtooth map

10.1007/bf01049033

Crossref journal-article

Springer Science and Business Media LLC

Journal of Statistical Physics (297)

Bibliography

Vaienti, S. (1992). Ergodic properties of the discontinuous sawtooth map. Journal of Statistical Physics, 67(1â2), 251â269.

Authors 1

S. Vaienti (first)

References 26 Referenced 22

I. C. Percival and F. Vivaldi, A linear code for the sawtooth and cat maps,Physica D 27:373?386 (1987). (10.1016/0167-2789(87)90037-6) / Physica D by I. C. Percival (1987)
N. Bird and F. Vivaldi, Periodic orbits of the sawtooth maps,Physica D 30:164 (1988). (10.1016/0167-2789(88)90104-2) / Physica D by N. Bird (1988)
I. Dana, Hamiltonian transport on unstable periodic orbits,Physica D 39:205?230 (1989). (10.1016/0167-2789(89)90005-5) / Physica D by I. Dana (1989)
Q. Chen, I. Dana, J. D. Meiss, N. W. Murray, and I. C. Percival, Resonances and transport in the sawtooth map,Physica D 46:217?240 (1990). (10.1016/0167-2789(90)90037-P) / Physica D by Q. Chen (1990)
V. Arnold and A. Avez,Ergodic Problems of Classical Mechanics (Benjamin, New York, 1968). / Ergodic Problems of Classical Mechanics by V. Arnold (1968)
J. R. Cary and J. D. Meiss, Rigorously diffusive deterministic map,Phys. Rev. A 24:2624?2628 (1981). (10.1103/PhysRevA.24.2624) / Phys. Rev. A by J. R. Cary (1981)
Ya. G. Sinai and N. I. Chernov, Ergodic properties of some systems of two-dimensional disks and of three-dimensional balls,Sov. Math. Surv. 42:153?174 (1987). (10.1070/RM1987v042n05ABEH001471) / Sov. Math. Surv. by Ya. G. Sinai (1987)
A. Kràmli, N. Simànyi, and D. Szàsz, Ergodic properties of semi-dispersing billiards: I?Two cylindric scatterers in the 3D torus,Nonlinearity 2:311?326 (1989). (10.1088/0951-7715/2/2/007) / Nonlinearity by A. Kràmli (1989)
A. Kràmli, N. Simànyi, and D. Szàsz, ?Transversal? fundamental theorem for semidispersing billiards,Commun. Math. Phys. 129:535?560 (1990). (10.1007/BF02097105) / Commun. Math. Phys. by A. Kràmli (1990)
L. A. Bunimovich, A theorem on ergodicity of two-dimensional hyperbolic billiards,Commun. Math. Phys. 130:599?621 (1990). (10.1007/BF02096936) / Commun. Math. Phys. by L. A. Bunimovich (1990)
C. Liverani and M. Wojtkowski, private communication.
J. Bellissard and S. Vaienti, Rigorous diffusion properties for the sawtooth map,Commun. Math. Phys., to appear. (10.1007/BF02099181)
E. Hopf, Statistik der geodätischen Linien in Mannigfaltigkeiten negativer Krümmung,Ber. Verch. Akad. Wiss. Leipzig 91:261?304 (1939); see also B. Weiss, The geodesic flow on surfaces of negative curvature, inDynamical Systems: Theory and Applications (1975). / Ber. Verch. Akad. Wiss. Leipzig by E. Hopf (1939)
M. Wojtkowski, A model problem with the coexistence of stochastic and integrable behaviour,Commun. Math. Phys. 80:453?464 (1981); On the ergodic properties of piecewise linear perturbations of the twist maps,Ergodic Theory Dynam. Syst. 2:525?542 (1983). (10.1007/BF01941656) / Commun. Math. Phys. by M. Wojtkowski (1981)
M. Wojtkowski, Linked twist mappins have the K-property,Ann. N. Y. Acad. Sci. 357:65?76 (1980). (10.1111/j.1749-6632.1980.tb29676.x) / Ann. N. Y. Acad. Sci. by M. Wojtkowski (1980)
Ya. G. Sinai, Dynamical systems with elastic reflections,Sov. Math. Surv. 5:141?192 (1970). / Sov. Math. Surv. by Ya. G. Sinai (1970)
L. A. Bunimovich and Ya. G. Sinai, On the main theorem of the ergodic theory of dispersing billiards,Mat. Sb. 90:415?431 (1973). / Mat. Sb. by L. A. Bunimovich (1973)
L. A. Bunimovich, On the ergodic properties of nowhere dispersing billiards,Commun. Math. Phys. 65:295?312 (1979). (10.1007/BF01197884) / Commun. Math. Phys. by L. A. Bunimovich (1979)
G. Gallavotti, Lectures on the billiard, inDynamical Systems: Theory and Applications (1975).
G. Gallavotti and D. Ornstein, Billiards and Bernoulli schemes,Commun. Math. Phys. 38:83?101 (1974). (10.1007/BF01651505) / Commun. Math. Phys. by G. Gallavotti (1974)
P. Collet and Y. Levy, Ergodic properties of the Lozi mappings,Commun. Math. Phys. 93:461?481 (1984). (10.1007/BF01212290) / Commun. Math. Phys. by P. Collet (1984)
L. S. Young, Bowen-Ruelle measures for certain piecewise hyperbolic maps,Trans. Am. Math. Soc. 287:41 (1985). (10.1090/S0002-9947-1985-0766205-1) / Trans. Am. Math. Soc. by L. S. Young (1985)
M. Rychlik, Théorie ergodique, mesures invariantes et principe variationnel pour les applications de Lozi,C. R. Acad. Sci. Paris (1983).
R. Burton and R. W. Easton, Ergodicity of linked twist maps, inLecture Notes in Mathematics, No. 819 (1980), p. 35. (10.1007/BFb0086978) / Lecture Notes in Mathematics by R. Burton (1980)
F. Przytycki, Example of conservative diffeomorphisms of the two-dimensional torus with coexistence of elliptic and stochastic behaviour,Ergodic Theory Dynam. Syst. 2:439?463 (1982). (10.1017/S0143385700001711) / Ergodic Theory Dynam. Syst. by F. Przytycki (1982)
A. Katok and J.-M. Strelcyn, Smooth maps with singularities, inLecture Notes in Mathematics, No. 1222 (1986), p. 283. / Lecture Notes in Mathematics by A. Katok (1986)

Dates

Type	When
Created	20 years, 7 months ago (Jan. 30, 2005, 7:25 a.m.)
Deposited	6 years, 4 months ago (April 29, 2019, 7:12 p.m.)
Indexed	1 year, 7 months ago (Feb. 1, 2024, 6:57 p.m.)
Issued	33 years, 5 months ago (April 1, 1992)
Published	33 years, 5 months ago (April 1, 1992)
Published Print	33 years, 5 months ago (April 1, 1992)

Funders 0

None

BibTeX

@article{Vaienti_1992, title={Ergodic properties of the discontinuous sawtooth map}, volume={67}, ISSN={1572-9613}, url={http://dx.doi.org/10.1007/bf01049033}, DOI={10.1007/bf01049033}, number={1–2}, journal={Journal of Statistical Physics}, publisher={Springer Science and Business Media LLC}, author={Vaienti, S.}, year={1992}, month=apr, pages={251–269} }

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