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It is known that all non-hyperbolic robustly transitive sets Λφ 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 Λφ form an interval in ℕ. We also prove that the homoclinic classes of two periodic points in Λφ are robustly equal. Finally, we describe what sort of homoclinic tangencies may appear in Λφ by studying its dominated splittings.


This article was originally published in Astérisque, 286 (2003), 187-222, available at



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