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Periodic points and homoclinic classes

  • F. ABDENUR (a1), CH. BONATTI (a2), S. CROVISIER (a3), L. J. DÍAZ (a4) and L. WEN (a5)
  • DOI:
  • Published online: 20 December 2006

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.

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Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
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