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arXiv · 1208.3489

Symbolic Extensions and dominated splittings for Generic C^1-Diffeomorphisms

A. Arbieto·A. Armijo·T. Catalan·L. Senos
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Abstract

Let Diff^1(M) be the set of all C^1-diffeomorphisms f : M \rightarrow M, where M is a compact boundaryless d-dimensional manifold, d \geq 2. We prove that there is a residual subset R of Diff^1(M) such that if f \in 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 E\oplusF1 \oplus...\oplusFk \oplusG, where Fi is not hyperbolic and one-dimensional, or f|H(p) has no symbolic extensions.

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A. Arbieto, A. Armijo, T. Catalan, L. Senos. 2012-08-16. Symbolic Extensions and dominated splittings for Generic C^1-Diffeomorphisms. https://arxiv.org/abs/1208.3489

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