Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-28T03:50:28.006Z Has data issue: false hasContentIssue false
  • English
  • Français

Some ergodic properties of commuting diffeomorphisms

Published online by Cambridge University Press:  19 September 2008

Huyi Hu
Huyi Hu
Affiliation:
Department of Mathematics, University of Arizona, Tucson, AZ 85721, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

For a smooth ℤ2-action on a C∞ compact Riemannian manifold M, we discuss its ergodic properties which include the decomposition of the tangent space of M into subspaces related to Lyapunov exponents, the existence of Lyapunov charts, and the subadditivity of entropies.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 13 , Issue 1 , March 1993 , pp. 73 - 100
Copyright
Copyright © Cambridge University Press 1993

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[BK]Brin, M. & Katok, A.. On local entropy. Springer Lecture Notes in Mathematics 1007. Springer, Berlin-New York, 1983, pp. 30–38.Google Scholar
[G]Goodwyn, L.. Some counter-examples in topological entropy. Topology 11 (1972), 377–385.CrossRefGoogle Scholar
[K]Katok, A.. Lyapunov exponents, entropy and periodic orbits for difleomorphisms. Publ. Math. I.H.E.S. 51 (1980), 137–174.CrossRefGoogle Scholar
[LS]Ledrappier, F. & Strelcyn, J.-M.. Estimation from below in Pesin's entropy formula. Ergod. Th. & Dynam. Sys. 2 (1982), 203–219.Google Scholar
[LY]Ledrappier, F. & Young, L.-S.. The metric entropy of diffeomorphisms. Ann. Math. 122 (1985), 509–574.Google Scholar
[M]Mañé, R.. A proof of Pesin's formula. Ergod. Th. & Dynam. Sys. 1 (1981), 95–102.Google Scholar
[N]Newhouse, S. E.. Continuity properties of entropy. Ann. Math. 129 (1989), 215–235.Google Scholar
[O]Oseledec, V. I.. A multiplicative ergodic theorem. Lyapunov characteristic numbers for dynamical systems. Trans. Moscow Math. Soc. 19 (1968), 197–221.Google Scholar
[P]Pesin, Ya. B.. Families of invariant manifolds corresponding to non-zero characteristic exponents. Math. USSR Izvestija 10 (1978), 1261–1305.Google Scholar
[Ro]Rohlin, V. A.. Lectures on the theory of entropy of transformations with invariant measures. Russ. Math. Surveys 22 (1967), 1–54.CrossRefGoogle Scholar
[Ru]Ruelle, D.. Ergodic theory of differentiable dynamical systems. Publ. Math. I.H.E.S. 50 (1979), 27–58.CrossRefGoogle Scholar
[W]Walters, P.. An Introduction to Ergodic Theory. Springer-Verlag, New York, 1981.Google Scholar