Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-27T04:22:07.095Z Has data issue: false hasContentIssue false
  • English
  • Français

Entropy of expansive flows

Published online by Cambridge University Press:  19 September 2008

Romeo F. Thomas
Romeo F. Thomas
Affiliation:
Department of Mathematical Sciences, George Mason University, 4400 University Drive, Fairfax, Virginia 22030, USA
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.

Let h(φ) be the topological entropy of a real continuous flow φ on a compact metric space X. Introducing an equivalent definition for the topological entropy on an expansive real flow enables us to investigate the topological entropies of mutually conjugate expansive flows and estimate the periodic orbits of an expansive flow which has the pseudo-orbit tracing property.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 7 , Issue 4 , December 1987 , pp. 611 - 625
Copyright
Copyright © Cambridge University Press 1987

References

REFERENCES

[1]Bowen, R.. Topological entropy and Axiom A. Proc. Symp. Pure Math. 14 (1970), 23–41.Google Scholar
[2]Bowen, R.. Entropy for group endomorphisms and homogeneous spaces. Trans. Amer. Math. Soc. 153 (1970), 401–414.Google Scholar
[3]Bowen, R.. Periodic orbits for hyperbolic flows. Amer. J. Math. 94 (1972), 1–30.CrossRefGoogle Scholar
[4]Bowen, R.. Entropy-expansive maps. Trans. Amer. Math. Soc. 164 (1972), 323–331.CrossRefGoogle Scholar
[5]Bowen, R. & Walters, P.. Expansive one parameter flows. J. Diff. Eq. 12 (1972), 180–193.Google Scholar
[6]Humphries, P. D.. Change of velocity in dynamical systems. J. London Math. Soc. (2), 7 (1974), 747–757.Google Scholar
[7]Ohno, T.. A weak equivalence and topological entropy. Publ. RIMS Kyoto Univ. 16 (1980), 289–298.CrossRefGoogle Scholar
[8]Thomas, R.. Stability properties of one parameter flows. Proc. London Math. Soc. (3), 45 (1982), 479–505.Google Scholar
[9]Thomas, R.. Topological stability: some fundamental properties. J. Diff. Eq. 59 (1985), 103–122.CrossRefGoogle Scholar
[10]Walters, P.. Ergodic Theory: Introductory Lectures. Springer Lecture Notes in Maths 458 (1975).CrossRefGoogle Scholar