Hostname: page-component-6766d58669-bkrcr Total loading time: 0 Render date: 2026-05-20T20:06:13.405Z Has data issue: false hasContentIssue false
  • English
  • Français

Hartman’s theorem for hyperbolic sets

Published online by Cambridge University Press:  22 January 2016

Masahiro Kurata
Masahiro Kurata*
Affiliation:
Hokkaido University
Rights & Permissions [Opens in a new window]

Extract

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.

Hartman proved that a diffeomorphism is topologically conjugate to a linear map on a neighbourhood of a hyperbolic fixed point ([3]). In this paper we study the topological conjugacy problem of a diffeomorphism on a neighbourhood of a hyperbolic set, and prove that for any hyperbolic set there is an arbitrarily slight extension to which a sub-shift of finite type is semi-conjugate.

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 67 , August 1977 , pp. 41 - 52
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1977

References

[1] Bowen, R.: Markov partitions for Axiom A diffeomorphisms, Amer. Jour. Math., 92 (1970), 725–747.CrossRefGoogle Scholar
[2] Bowen, R.: Markov partitions and minimal sets for Axiom A diffeomorphisms, Amer. Jour. Math., 92 (1970), 907–918.CrossRefGoogle Scholar
[3] Hartman, P.: Ordinary differential equations, Wiley, 1964.Google Scholar
[4] Hirsch, M. W. and Pugh, C.: Stable manifolds and hyperbolic sets, Global Analysis, Proc. Symp. Pure Math., A.M.S., 14 (1970), 133–167.Google Scholar
[5] Nitecki, Z.: Differentiate dynamics, MIT Press, 1971.Google Scholar
[6] Pugh, C.: On a theorem of P. Hartman, Amer. Jour. Math., 91 (1969), 363–367.Google Scholar
[7] Sinai, Ja. G.: Markov partitions and C-diffeomorphisms, Functional Analysis and its applications, 2 (1968), 61–82.Google Scholar