Periodic points and homoclinic classes

• Autores: F. Abdenur, Ch. Bonatti, Sylvain Crovisier, Lorenzo Justiniano Díaz Casado, L. Wen
• Localización: Ergodic theory and dynamical systems, ISSN 0143-3857, Vol. 27, Nº 1, 2007, págs. 1-22
• Idioma: inglés
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• Resumen

  • We prove that there is a residual subset $\mathcal{I}$ of ${\rm Diff}^1({\it M})$ such that any homoclinic class of a diffeomorphism $f\in \mathcal{I}$ having saddles of indices $\alpha$ and $\beta$ contains a dense subset of saddles of index $\tau$ for every $\tau\in [\alpha,\beta]\cap \mathbb{N}$. We also derive some consequences from this result about the Lyapunov exponents of periodic points and the sort of bifurcations inside homoclinic classes of $C^1$-generic diffeomorphisms.