Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-24T23:56:39.715Z Has data issue: false hasContentIssue false
  • English
  • Français

Gibbs measures for partially hyperbolic attractors

Published online by Cambridge University Press:  19 September 2008

Ya. B. Pesin  and
Ya. G. Sinai
Ya. B. Pesin
Affiliation:
L. D. Landau Institute for Theoretical Physics, Academy of Sciences of the USSR, 142432 Chemogolovka, Moscow Region, USSR
Ya. G. Sinai
Affiliation:
L. D. Landau Institute for Theoretical Physics, Academy of Sciences of the USSR, 142432 Chemogolovka, Moscow Region, USSR
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We consider iterates of absolutely continuous measures concentrated in a neighbourhood of a partially hyperbolic attractor. It is shown that limit points can be measures which have conditional measures of a special form for any partition into subsets of unstable manifolds.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 2 , Issue 3-4 , December 1982 , pp. 417 - 438
Copyright
Copyright © Cambridge University Press 1982

References

REFERENCES

[1]Anosov, D. V.. On tangent fields of transversal foliation in ‘U’-systems. Mat. Zametky 2 No 5 (1967), 539–548.Google Scholar
[2]Anosov, D. V. & Sinai, Ya. G.. Some smooth ergodic systems. Russ. Math. Surveys 22 No 5 (1967), 107–172.CrossRefGoogle Scholar
[3]Brin, M. & Pesin, Ya.. Partially hyperbolic dynamical systems. Izv. Acad. Nauk SSSR ser mat. No 1 (1974), 170–212.Google Scholar
[4]Brin, M.. The estimation below of the entropy of smooth dynamical systems. Functional Anal. 8 No 3 (1974), 71–72.Google Scholar
[5]Sinai, Ya. G.. Lectures on Ergodic Theory. Erevan State Univ. Press: Erevan, 1973.Google Scholar
[6]Sinai, Ya. G.. Dynamical systems with Lebesgue spectrum II. Izv. Acad. Nauk SSSR 30 No 1 (1968), 15–68.Google Scholar
[7]Pesin, Ya. B.. Characteristic Lyapunov exponents and smooth ergodic theory. Russ. Math. Surveys. 32 No 4 (1977), 55–114.CrossRefGoogle Scholar
[8]Pesin, Ya. B.. Description of π-partition for diffeomorphism with invariant measure. Mat. Zametky 21 No 6 (1977), 29–44Google Scholar
[9]Pesin, Ya. B.. Families of invariant manifolds for dynamical systems with non-zero characteristic Lyapunov exponents. Izv. Acad. Nauk SSSR 40 No 6 (1976), 1332–1379.Google Scholar
[10]Margulis, G. A.. On some problems in the theory of U-systems. Dissertation, Moscow State Univ. 1970.Google Scholar
[11]Mather, J.. Characterization of Anosov diffeomorphisms. Indag. Math. 30 No 5 (1968), 479–483.CrossRefGoogle Scholar
[12]Katok, A.. Local properties of hyperbolic sets. Appendix to the Russian translation of the book by Z. Nitecki. Introduction to Differential Dynamics. Moscow: Mir Press, 1975.Google Scholar
[13]Katok, A.. Lyapunov exponents, entropy and periodic orbits for diffeomorphisms. Publ. Math. 51 (1980), 137–173.CrossRefGoogle Scholar
[14]Hirsch, M., Pugh, P. & Shub, M.. Invariant manifolds. Bull. Amer. Math. Soc. 76 (1970), 1015–1019.CrossRefGoogle Scholar
[15]Bowen, R.. Equilibrium states and the ergodic theory of Anosov diffeomorphisms. Lecture Notes, No. 470, 1975, p. 108.Google Scholar
[16]Bowen, R. & Ruelle, D.. The ergodic theory of axiom A flows. Invent. Math. 29 (1975), 181–202.CrossRefGoogle Scholar