Symbolic Extensions and dominated splittings for Generic C^1-Diffeomorphisms
Dynamical Systems
2012-08-20 v1
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.
Cite
@article{arxiv.1208.3489,
title = {Symbolic Extensions and dominated splittings for Generic C^1-Diffeomorphisms},
author = {A. Arbieto and A. Armijo and T. Catalan and L. Senos},
journal= {arXiv preprint arXiv:1208.3489},
year = {2012}
}