The boundary of hyperbolicity for Henon-like families
Dynamical Systems
2012-11-07 v2
Abstract
We consider C^{2} Henon-like families of diffeomorphisms of R^{2} and study the boundary of the region of parameter values for which the nonwandering set is uniformly hyperbolic. Assuming sufficient dissipativity, we show that the loss of hyperbolicity is caused by a first homoclinic or heteroclinic tangency and that uniform hyperbolicity estimates hold uniformly in the parameter up to this bifurcation parameter and even, to some extent, at the bifurcation parameter.
Keywords
Cite
@article{arxiv.math/0502235,
title = {The boundary of hyperbolicity for Henon-like families},
author = {Yongluo Cao and Stefano Luzzatto and Isabel Rios},
journal= {arXiv preprint arXiv:math/0502235},
year = {2012}
}
Comments
32 pages, 11 figures. Several minor revisions, additional figures, clarifications of some arguments