Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

Journals Home Search My Subscriptions Subscribe
Previous issue | This issue | Most recent issue | All issues (1950–Present) | Next issue | Previous article | Articles in press | Recently published articles | Next article
Request Permissions
 
 

 

Diffeomorphisms with persistency


Author: Kazuhiro Sakai
Journal: Proc. Amer. Math. Soc. 124 (1996), 2249-2254
MSC (1991): Primary 54H20, 58F10, 58F15
DOI: https://doi.org/10.1090/S0002-9939-96-03275-3
MathSciNet review: 1317049
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The $C^1$ interior of the set of all diffeomorphisms satisfying Lewowicz's persistency is characterized as the set of all diffeomorphisms satisfying Axiom A and the strong transversality condition.

References [Enhancements On Off] (What's this?)

  • 1. N. Aoki, The set of Axiom A diffeomorphisms with no cycle, Bol. Soc. Bras. Mat. 23-New Series (1992), 21-65. MR 94d:58080
  • 2. J. Franks, Necessary conditions for stability of diffeomorphisms, Trans. A.M.S., 158 (1971), 301-308. MR 44:1042
  • 3. M. Gerber and A. Katok, Smooth models of Thurston's pseudo-Anosov maps, Ann. Scient. Éc. Norm. Sup., $4^e$ série, t. 15, 1982, 173-204. MR 84e:58056
  • 4. S. Hayashi, Diffeomorphisms in ${\mathcal F}^1(M)$ satisfy Axiom A, Ergod. Th. & Dyn. Sys. 12 (1992), 233-253. MR 94d:58081
  • 5. J. Lewowicz, Persistence in expansive systems, Ergod. Th. & Dyn. Sys. 3 (1983), 567-578. MR 85m:58140
  • 6. R. Mañé, Expansive Diffeomorphisms, Dynamical Systems-Warwick, 1974, (ed. by A. Manning), Lecture Notes in Math. 468, Springer, 1975, 162-174. MR 58:31263
  • 7. K. Moriyasu, The topological stability of diffeomorphisms, Nagoya Math. J. 123 (1991), 91-102. MR 92g:58067
  • 8. C. Robinson, Stability theorems and hyperbolicity in dynamical systems, Rocky Mountain J. Math., 7 (1977), 425-437. MR 58:13200
  • 9. K. Sakai, Pseudo-orbit tracing property and strong transversality of diffeomorphisms on closed manifolds, Osaka J. Math. 31(1994), 373-386. CMP 95:02

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 54H20, 58F10, 58F15

Retrieve articles in all journals with MSC (1991): 54H20, 58F10, 58F15

Additional Information

Kazuhiro Sakai
Affiliation: Department of Mathematics, Kanagawa University, Rokkakubashi, Kanagawa-Ku, Yokohama 221, Japan
Email: kazsaka@kani.cc.kanagawa.ac.jp

DOI: https://doi.org/10.1090/S0002-9939-96-03275-3
Keywords: Persistence, expansive, pseudo-Anosov map, Axiom A, Anosov diffeomorphism
Received by editor(s): October 12, 1994
Received by editor(s) in revised form: January 6, 1995
Communicated by: Mary Rees
Article copyright: © Copyright 1996 American Mathematical Society