Polynomial diffeomorphisms of C2. VIII: Quasi-expansion
By Eric Bedford, J. Smillie. 2001
50 citations recorded by the source corpus.
We introduce the notion of quasi-expansion in the context of polynomial diffeomorphisms of C 2 . Like hyperbolic diffeomorphisms, quasi-expanding maps have uniformly large multipliers at saddle points. On the other hand, unlike the hyperbolic case, quasi-expanding maps can have tangencies between stable and unstable manifolds. We characterize quasi-expansion in a number of ways and develop some of the structure they possess. Quasi-expansion was motivated by the study of real polynomial diffeomorphisms of maximal entropy, and our study of maximal entropy diffeomorphisms relies on the results of this paper.
Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/ff6adfcd9f5fc8b77fe7058836b58ab916b7dae4
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In Geometry and Topology
- Eric Bedford
- J. Smillie
- Serge Cantat
- Curtis T. McMullen
- Matt Bainbridge
- John Lesieutre
- Barak Weiss
- Christopher J. Leininger
In Mathematical Physics
- Eric Bedford
- J. Smillie
- Serge Cantat
- Curtis T. McMullen
- Matt Bainbridge
- John Lesieutre
- Barak Weiss
- Christopher J. Leininger
In Statistical and Nonlinear Physics
- Eric Bedford
- J. Smillie
- Serge Cantat
- Curtis T. McMullen
- Matt Bainbridge
- Barak Weiss
- Christopher J. Leininger
Citations in the corpus
- Real polynomial diffeomorphisms with maximal entropy: Tangencies (2001, methodology): “By [ BLS , Th. 9.6] A is dense in K ∩U. It follows from the local product structure that the transverse intersections between W u(p) and W s”