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math.DS2004
Decay of correlations for Henon maps
Tien-Cuong Dinh
We show, for a class of automorphisms of C^k, that their equilibrium measures are exponentially mixing. In particular, this holds for (generalized) Henon maps.
math.DS2004★ 1 cited
Hausdorff dimension and conformal measures of Feigenbaum Julia sets
Artur Avila, Mikhail Lyubich
We show that contrary to anticipation suggested by the dictionary between rational maps and Kleinian groups and by the ``hairiness phenomenon'', there exist many Feigenbaum Julia s…
math.DS2004★ 3 cited
Weak mixing for interval exchange transformations and translation flows
Artur Avila, Giovanni Forni
We show that a typical interval exchange transformation is either weakly mixing or it is an irrational rotation. We also conclude that a typical translation flow on a surface of ge…