-
Polynomial diffeomorphisms of C2. VIII: Quasi-expansion
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 124, Number 2, April 2002
- pp. 221-271
- 10.1353/ajm.2002.0008
- Article
- Additional Information
- Purchase/rental options available:
We introduce the notion of quasi-expansion in the context of polynomial diffeomorphisms of C2. 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.