Periodic points and homoclinic classes

International audienceWe 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