C1-stably shadowable chain components

Ergodic Theory and Dynamical Systems

Volumn 28, Issue 3, 2008, Pages 987-1029

  Sakai, Kazuhiro ^a  

^a UTSUNOMIYA UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

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EID: 44249110058     PISSN: 01433857     EISSN: 14694417     Source Type: Journal    
DOI: 10.1017/S0143385707000570     Document Type: Article

References (38)

1. F. Abdenur. Generic robustness of spectral decompositions. Ann. Sc. École Norm. Sup., Ser. 4 36 (2003), 213-224.
2. F. Abdenur, C. Bonatti, S. Crovisier and L. J. Díaz. Generic diffeomorphisms on compact surfaces. Fund. Math. 187 (2005), 127-159.
3. 1 topology. Discrete Contin. Dyn. Syst. 17 (2007), 223-245.
4. N. Aoki. On homeomorphisms with pseudo-orbit tracing property. Tokyo J. Math. 6 (1983), 329-334.
5. C. Bonatti and S. Crovisier. Récurrence et géné ricité. Invent. Math. 158 (2004), 33-104.
6. C. Bonatti and L. J. Díaz. Persistence of transitive diffeomorphisms. Ann. of Math. 143 (1995), 367-396.
7. C. Bonatti, L. J. Díaz and G. Turcat. Pas de «Shadowing lemma» pour les dynamiques partiellment hyperboliques. C. R. Acad. Sci. Paris, Ser. I 330 (2000), 587-592.
8. 1 -generic dichotomy for diffeomorphisms: Weak forms of hyperbolicity or infinitely many sinks or sources. Ann. of Math. 158 (2003), 355-418.
9. C. Bonatti, L. J. Díaz and M. Viana. Dynamics Beyond Uniform Hyperbolicity (Encyclopedia of Mathematical Sciences, Mathematical Physics, 102). Springer, Berlin, 2005.
10. K. Burns, C. Pugh, M. Shub and A. Wilkinson. Recent results about stable ergodicity. Smooth Ergodic Theory and its Applications (Seattle, WA, 1999) (Proceedings Symposia in Pure Mathematics, 69). American Mathematical Society, Providence, RI, 2001, pp. 327-366.
11. C. Conley. Isolated Invariant Sets and Morse Index (CBMS Regional Conferences Series in Mathematics, 38). American Mathematical Society, Providence, RI, 1978.
12. S. Crovisier. Saddle-node bifurcations for hyperbolic sets. Ergod. Th. & Dynam. Sys. 22 (2002), 1079-1115.
13. L. J. Díaz. Robust nonhyperbolic dynamics and heterodimensional cycles. Ergod. Th. & Dynam. Sys. 15 (1995), 291-315.
14. L. J. Díaz, E. R. Pujals and R. Ures. Partial hyperbolicity and robust transitivity. Acta Math. 183 (1999), 1-43.
15. L. J. Díaz and J. Rocha. Partially hyperbolic and transitive dynamics generated by heteroclinic cycles. Ergod. Th. & Dynam. Sys. 21 (2001), 25-76.
16. J. Franks. Necessary conditions for stability of diffeomorphisms. Trans. Amer. Math. Soc. 158 (1971), 301-308.
17. M. Hirsch, C. Pugh and M. Shub. Invariant Manifolds (Lecture Notes in Mathematics, 583). Springer, Berlin, 1977.
18. A. Katok and B. Hasselblatt. Introduction to the Modern Theory of Dynamical Systems (Encyclopedia of Mathematics and its Applications, 54). Cambridge University Press, Cambridge, 1995.
19. R. Mañé. Expansive diffeomorphisms. Proc. Symp. on Dynamical Systems (University of Warwick, 1974) (Lecture Notes in Mathematics, 468). 1975, pp. 162-174.
20. R. Mañé. Contributions to the stability conjecture. Topology 17 (1978), 383-396.
21. R. Mañé. Persistent manifolds are normally hyperbolic. Trans. Amer. Math. Soc. 246 (1978), 261-283.
22. R. Mañé. An ergodic closing lemma. Ann. of Math. 116 (1982), 503-540.
23. K. Moriyasu. The topological stability of diffeomorphisms. Nagoya Math. J. 123 (1991), 91-102.
24. M. J. Pacifico, E. R. Pujals and J. L. Vieitez. Robustly expansive homoclinic classes. Ergod. Th. & Dynam. Sys. 25(2005), 271-300.
25. J. Palis and F. Takens. Hyperbolicity and Sensitive Chaotic Dynamics at Homoclinic Bifurcations (Cambridge Studies in Advanced Mathematics, 35). Cambridge University Press, Cambridge, 1993.
26. S. Yu. Pilyugin. Shadowing in Dynamical Systems (Lecture Notes in Mathmatics, 1706). Springer, Berlin, 1999.
27. S. Yu. Pilyugin, A. A. Rodionova and K. Sakai. Orbital and weak shadowing properties. Discrete Contin. Dyn. Syst. 9 (2003), 287-308.
28. 0 transversality and shadowing properties. Proc. Steklov Inst. Math. 256 (2007), 290-305.
29. E. R. Pujals and M. Sambarino. Homoclinic tangencies and hyperbolicity for surface diffeomorphisms. Ann. of Math. 151 (2000), 961-1023.
30. C. Robinson. Stability theorems and hyperbolicity in dynamical systems. Rocky Mountain J. Math. 7 (1977), 425-137.
31. K. Sakai. Pseudo-orbit tracing property and strong transversality of diffeomorphisms on closed manifolds. Osaka J. Math. 31 (1994), 373-386.
32. K. Sakai. Shadowing Property and Transversality Condition (Proc. Int. Conf. on Dynamical Systems and Chaos, 1). World Scientific, Singapore, 1995, pp. 233-238.
33. 2 stable shadowing. Dyn. Syst. 17 (2002), 235-241.
34. 1-persistently expansive homoclinic classes. Discrete Contin. Dyn. Syst. 14(2006), 465-481.
35. T. Shimomura. On a structure of discrete dynamical systems from the view point of chain components and some applications. Japan. J. Math. (N. S.) 15 (1989), 99-126.
36. S. Smale. Diffeomorphisms with many periodic points. Differential and Combinatorial Topology. Princeton University Press, Princeton, NJ, 1965, pp. 63-80.
37. L. Wen. Homoclinic tangencies and dominated splittings. Nonlinearity 15 (2002), 1445-1469.
38. G.-C. Yuan and J. A. Yorke. An open set of maps for which every point is absolutely nonshadowable. Proc. Amer. Math. Soc. 128 (2000), 909-918.