The boundary of hyperbolicity for Henon-like families

Details The boundary of hyperbolicity for Henon-like families The boundary of hyperbolicity for Henon-like families

2005-02-11

arxiv.org/abs/math/0502235v2

Mathematics

Dynamical Systems

32 pages, 11 figures. Several minor revisions, additional figures, clarifications of some arguments

Scientific paper

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.

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