Periodic points and homoclinic classes

Abstract : We prove that there is a residual subset I of Diff such that any homoclinic class of a diffeomorphism f in I having saddles of indices alpha and beta contains a dense subset of saddles of index tau for every tau in [alpha,beta] cap NN. We also derive some consequences from this result about the Lyapunov exponents of periodic points and the sort of bifurcations inside homoclinic classes of generic diffeomorphisms.
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Flavio Abdenur, Christian Bonatti, Sylvain Crovisier, Lorenzo J. Díaz, Lan Wen. Periodic points and homoclinic classes. Ergodic Theory and Dynamical Systems, Cambridge University Press (CUP), 2007, 27 (1), pp.1-22. ⟨10.1017/S0143385706000538⟩. ⟨hal-00538123⟩

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