Homoclinic classes for generic C1 vector fields

Ergodic Theory and Dynamical Systems

Volumn 23, Issue 2, 2003, Pages 403-415

  Carballo, C M ^a   Morales, C A ^b   Pacifico, M J ^b  

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

^b FEDERAL UNIVERSITY OF RIO DE JANEIRO   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0037398834     PISSN: 01433857     EISSN: None     Source Type: Journal    
DOI: 10.1017/s0143385702001116     Document Type: Article

References (19)

1. 1. Ergod. Th. & Dynam. Sys. 21 (2001), 339-381.
2. F. Béguin, C. Bonatti and J. L. Vieitez. Construction de flots de Smale en dimension 3. Ann. Fac. Sci. de Toulouse Math. 6 (1999), 369-410.
3. N. P. Bhatia and G. P. Szego. Stability Theory of Dynamical Systems. Springer, Heidelberg, 1979.
4. C. Bonatti and L. J. Díaz. Connexions heterocliniques et generiecité d'une infinité de puits ou de sources. Ann. Sci. École Norm. Sup. 32 (1999), 135-150.
5. 1-dichotomy for diffeomorphisms: weak forms of hyperbolicity or infinitely many sinks or sources. Preprint, 1999.
6. W. de Melo and J. Palis. Geometric Theory of Dynamical Systems - An Introduction. Springer, Berlin, 1982.
7. 1 make or break lemma. Bull. Braz. Math. Soc. 31 (2000), 337-350.
8. 1 stability and Ω-stability conjectures for flows. Ann. Math. 145 (1997), 81-137.
9. S. Hayashi. Hyperbolicity, stability, and the creation of homoclinic points. Documenta Math., Extra Volume ICM 2 (1998).
10. M. Hirsch, C. Pugh and M. Shub. Stable manifolds and hyperbolic sets. Proc. Symp. Pure Math. - Global Analysis 14 (1970), 133-163.
11. A. Katok and B. Hasselblatt. Introduction to the Modern Theory of Dynamical Systems. Cambridge University Press, Cambridge, 1995.
12. K. Kuratowski. Topology II. Academic Press - PWN-Polish Science Publishers, Warszawa, 1968.
13. S. T. Liao. On hyperbolicity properties of nonwandering sets of certain 3-dimensional differential systems. Acta Math. Sci. 3 (1983), 361-368.
14. R. Mañé. An ergodic closing lemma. Ann. Math. 116 (1982), 503-540.
15. C. A. Morales and M. J. Pacifico. Mixing attractors for 3-flows. Nonlinearity 14 (2001), 359-378.
16. J. Palis and F. Takens. Hyperbolicity and Sensitive-Chaotic Dynamics at Homoclinic Bifurcations. Cambridge University Press, Cambridge, 1993.
17. C. Pugh. An improved closing lemma and a general density theorem. Amer. J. Math. 89 (1967), 1010-1021.
18. 1-stability conjecture for flows. J. Diff. Eqns 129 (1995), 334-357.
19. 1 connecting lemmas. Trans. Amer. Math. Soc. 352 (2000), 5213-5230.