Symbolic Extensions and dominated splittings for Generic C1-Diffeomorphisms
Abstract
Let Diff1(M) be the set of all C1-diffeomorphisms f : M → M, where M is a compact boundaryless d-dimensional manifold, d ≥ 2. We prove that there is a residual subset R of Diff1(M) such that if f ∈ R and if H(p) is the homoclinic class associated with a hyperbolic periodic point p, then either H(p) admits a dominated splitting of the form E1 ... , where Fi is not hyperbolic and one-dimensional, or f|H(p) has no symbolic extensions.
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