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- Title
The boundary of hyperbolicity for H?non-like families.
- Authors
YONGLUO CAO; STEFANO LUZZATTO; ISABEL RIOS
- Abstract
AbstractWe consider C2H?non-like families of diffeomorphisms of $ \mathbb R^{2} $and study the boundary of the region of parameter values for which the non-wandering 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 parameterup to the bifurcation parameter and even, to some extent, at the bifurcation parameter.
- Subjects
DIFFEOMORPHISMS; DIFFERENTIAL topology; DIFFERENTIAL geometry; BIFURCATION theory; ESTIMATES
- Publication
Ergodic Theory & Dynamical Systems, 2008, Vol 28, Issue 4, p1049
- ISSN
0143-3857
- Publication type
Article
- DOI
10.1017/S0143385707000776