Partial hyperbolicity far from homoclinic bifurcations

By S. Crovisier. 2008

57 citations recorded by the source corpus.

Abstract We prove that any diffeomorphism of a compact manifold can be C 1 -approximated by a diffeomorphism which exhibits a homoclinic bifurcation (a homoclinic tangency or a heterodimensional cycle) or by a diffeomorphism which is partially hyperbolic (its chain-recurrent set splits into partially hyperbolic pieces whose centre bundles have dimensions less or equal to two). We also study in a more systematic way the central models introduced in Crovisier (in press) [10] .

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/b7871e65c0890d5149d49442321fafa74ae2f893

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. S. Crovisier
2. E. Pujals
3. C. Bonatti

In Mathematical Physics

1. S. Crovisier
2. E. Pujals
3. C. Bonatti
4. Shaobo Gan
5. Lorenzo J. Díaz
6. Nicolas Gourmelon

In Statistical and Nonlinear Physics

1. S. Crovisier
2. E. Pujals
3. C. Bonatti
4. Lorenzo J. Díaz
5. Shaobo Gan
6. Nicolas Gourmelon

Citations in the corpus

• Essential hyperbolicity and homoclinic bifurcations: a dichotomy phenomenon/mechanism for diffeomorphisms (2010, background): “Following [18,19] (see Theorems 4 and 5 below), it is concluded thatC1-far from homoclinic bifurcations, the aperiodic chain-recurrent classes are partially hyperbolic with a one-dimensional center bundle, and the homoclinic classes are partially hyperbolic with their center bundles being at most tw”