Robustly transitive sets and heterodimensional cycles

Authors

Christian Bonatti, Centre national de la recherche scientifique
Lorenzo J. Díaz, Pontifícia Universidade Católica do Rio de Janeiro
Enrique R. Pujals, CUNY Graduate CenterFollow
Jorge Rocha, Universidade do Porto

Document Type

Article

Publication Date

2003

Abstract

It is known that all non-hyperbolic robustly transitive sets Λ_φ have a dominated splitting and, generically, contain periodic points of different indices. We show that, for a C¹-dense open subset of diffeomorphisms φ, the indices of periodic points in a robust transitive set Λ_φ form an interval in ℕ. We also prove that the homoclinic classes of two periodic points in Λ_φ are robustly equal. Finally, we describe what sort of homoclinic tangencies may appear in Λ_φ by studying its dominated splittings.

Comments

This article was originally published in Astérisque, 286 (2003), 187-222, available at http://www.numdam.org/item/AST_2003__286_.pdf#page=216