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Mostly contracting di eomorphisms are the simplest
examples of robustly nonuniformly hyperbolic systems. This paper studies the mixing properties of mostly contracting di eomorphisms.
Dense properties of the space of the circle diffeomorphisms with a Liouville rotation number
circle diffeomorphism rotation number Liouville number conjugacy invariant measure fast approximation by conjugation
2011/9/23
Abstract: Given any Liouville number $\alpha$, it is shown that various subspaces are $C^\infty$-dense in the space of the orientation preserving $C^\infty$ diffeomorphisms of the circle with rotation...
Bernoulli equilibrium states for surface diffeomorphisms
Equilibrium measures Countable Markov partitions Bernoulli
2011/9/14
Abstract: Suppose f is a $C^{1+\alpha}$ surface diffeomorphism, and m is an equilibrium measure of a Holder continuous potential. We show that if m has positive metric entropy, then f is measure theor...
Embedding smooth and formal diffeomorphisms through the Jordan-Chevalley decomposition
local diffeomorphism normal form embedding flow
2011/9/14
Abstract: In [Xiang Zhang, The embedding flows of $C^{\infty}$ hyperbolic diffeomorphisms, J. Differential Equations 250 (2011), no. 5, 2283-2298] Zhang proved that any local smooth hyperbolic diffeom...