Robust heterodimensional cycles and C1-generic dynamics

Journal of the Institute of Mathematics of Jussieu

Volumn 7, Issue 3, 2008, Pages 469-525

  Bonatti, Christian ^a   Díaz, Lorenzo J ^b  

^a UNIVERSITÉ DE BOURGOGNE   (France)

^b PONTIFICAL CATHOLIC UNIVERSITY OF RIO DE JANEIRO   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 44149109395     PISSN: 14747480     EISSN: 14753030     Source Type: Journal    
DOI: 10.1017/S1474748008000030     Document Type: Article

References (44)

1. F. ABDENUR, Generic robustness of spectral decompositions, Annales Scient. Éc. Norm. Sup. 36 (2003), 212-224.
2. 1-topology, Discrete Contin Dynam. Syst. 17 (2007), 223-245.
3. F. ABDENUR, CH. BONATTI, S. CROVISIER AND L. J. DÍAZ, Generic diffeomorphisms on compact surfaces, Fund. Math. 187 (2005), 127-159.
4. F. ABDENUR, CH. BONATTI, S. CROVISIER, L. J. DÍAZ AND L. WEN, Periodic points and homoclinic classes, Ergod. Theory Dynam. Syst. 26 (2006), 1-22.
5. R. ABRAHAM AND S. SMALE, Nongenericity of Ω-stability, in Global analysis, Proceedings of Symposia in Pure Mathematics, Volume 14, pp. 5-8 (American Mathematical Society, Providence, RI, 1968).
6. 1-persistent homoclinic tangency for higher dimensions, Proc. Am. Math. Soc., in press.
7. CH. BONATTI AND S. CROVISIER, Récurrence et généricité, Invent. Math. 158 (2004), 33-104.
8. CH. BONATTI AND L. J. DÍAZ, Persistent non-hyperbolic transitive diffeormorphims, Annals Math. 143 (1995), 357-396.
9. CH. BONATTI AND L. J. DÍAZ, Connexions hétéroclines et généricité d'une infinité de puits on de sources, Annales Scient. Éc. Norm. Sup. 32 (1999), 135-150.
10. CH. BONATTI AND L. J. DÍAZ, On maximal transitive sets of generic diffeomorphis, Publ. Math. IHES 96 (2002), 171-197.
11. CH. BONATTI, L. J. DÍAZ AND M. VIANA, Discontinuity of the Hausdorff dimension of hyperbolic sets, C. R. Acad. Sci. Paris Ser. I 320 (1995), 713-718.
12. CH. BONATTI, L. J. DiAZ AND G. TURCAT, Pas de Shadowing Lemma pour les dynamiques partiellment hyperboliques, C. R. Acad. Sci. Paris Sér. I 330 (2000), 587-592.
13. 1-gencric dichotomy for diffeomorphisms: Weak forms of hyperbolicicity or infinitely many sinks or sources, Annals Math. 158 (2003), 355-418.
14. CH. BONATTI, L. J. DÍAZ, E. R. PUJALS AND J. ROCHA, Robustly transitive sets and heterodimensional cycles, Astérisque 286 (2003), 187-222.
15. CH. BONATTI, L. J. DÍAZ AND M. VIANA, Dynamics beyond uniform hyperbolicity, in Encyclopacdia of Mathematical Science (Mathematical Physics), Volume 102 (Springer, 2005).
16. 1 vector fields, Ergod. Theory Dynam. Syst. 23 (2003), 403-415.
17. C. CONLEY, Isolated invariant sets and the Morse index, CBMS Regional Conference Series in Mathematics, Volume 38 (American Mathematical Society, Providence, RI, 1978).
18. L. J. DÍAZ, Robust nonhyperbolic dynamics and heterodimensional cycles, Ergod. Theory Dynam. Syst. 15 (1995), 291-315.
19. L. J. DÍAZ, Persistence of cycles and non-hyperbolic dynamics at the unfolding of heterodimensional cycles, Nonlinearity 8 (1995), 693-715.
20. L. J. DÍAZ AND J. ROCHA, Nonconnected heterodimensional cycles: Bifurcation and stability, Nonlinearity 5 (1992), 1315-1341.
21. L. J. DÍAZ AND J. ROCHA, Partially hyperbolic and trnnsitive dynamics generated by heteroclinic cycles, Ergod. Theory Dynam. Syst. 25 (2001), 25-76.
22. L. J. DÍAZ AND J. ROCHA, Heterodimensional cycles, partial hyperbolicity and limit dynamics, Fund. Math. 174 (2002), 127-186.
23. L. J. DÍAZ AND R. URES, Persistent homoclinic tangencies and the unfolding of cycles, Annalles Inst. H. Poincaré Analyse Non Linéaire 11 (1994), 643-659.
24. L. J. DÍAZ, A. NOGUEIRA AND E. R. PUJALS, Heterodimensional tangencies, Nonlinearity 19 (2006), 2543-2566.
25. J. FRANKS, Necessary conditions for stability of diffeomorphisms, Trans. Am. Math. Soc. 158 (1971), 301-308.
26. 1-stability and Ω-stability conjectures for flows, Annals Math. 145 (1997), 81-137.
27. M. W. HIRSCH, C. C. PUGH AND M. SHUB, Invariant manifolds Lecture Notes in Mathematics Volume 583 (Springer, 1977).
28. R. MAÑÉ, Contributions to the stability conjecture, Topology, 17 (1978), 386-396.
29. R. MAÑÉ, An ergodic closing lemma, Annals Math. 116 (1982), 503-540.
30. 1-stable intersections of regular Cantor sets do not exist (April 2006; available at http://seminarios.impa.br/cgi-bin/ seminar_browse.cgi).
31. S. NEWHOUSE, Hyperbolic limit sets, Trans. Am. Math. Soc. 167 (1972), 125-150. diffeomorphisms, Publ. Math. IHES 50 (1979), 101-151.
32. S. NEWHOUSE, The abundance of wild hyperbolic sets and nonsmooth stable sets for diffeomorphisms, Publ. Math. IHES 50 (1979 , 101-151.
33. 2, in Global analysis, Proceedings of Symposia in Pure Mathematics, Volume 14, pp. 191-202 (American Mathematical Society, Providence, RI, 1968).
34. S. NEWHOUSE AND J. PALIS, Cycles and bifurcation theory, Astérisque 31 (1976), 43-140.
35. J. PALIS, A global view of dynamics and a conjecture on the denseness and finitude of attractors, Astérisque 261 (2000), 335-347.
36. J. PALIS AND F. TAKENS, Hyperbolicity and sensitive chaotic dynamics at homoclinic bifurcations: Fractal dimensions and infinitely many attractors, Cambridge Studies in Advanced Mathematics, Volume 35 (Cambridge University Press, 1993).
37. J. PALIS AND M. VIANA, High dimension diffeomorphisms displaying infinitely many sinks, Annals Math. 140 (1994), 207-250.
38. E. PUJALS AND M. SAMBARINO. Homoclinic tangencies and hyperbolicity for surface diffeomorphisms, Annals Math. 151 (2000), 961-1023.
39. N. ROMERO, Persistence of homoclinic tangencies in higher dimensions, Ergod. Theory Dynam. Syst. 15 (1995), 735-757.
40. 4, Lecture Notes in Mathematics, Volume 206, p. 39 (Springer, 1971).
41. R. C. SIMON, A 3-dimensional Abraham-Smale example, Proc. Am. Math. Soc. 34(2) (1972), 629-630.
42. S. SMALE, Differentiable dynamical systems, Bull. Am. Math. Soc. 73 (1967), 747-817.
43. 1 topology, Annales Scient. Éc. Norm. Sup. 28 (1995), 747-760.
44. G.-C. YUAN AND J. A. YORKE, An open set of maps for which every point is absolutely nonshadowable, Proc. Am. Math. Soc. 128 (3) (2000), 909-918.