4 citations · 19 across the 8 of their papers we have counts for
11 papers
Combinatorial rigidity for unicritical polynomials
Artur Avila, Jeremy Kahn, Mikhail Lyubich +1
We prove that any unicritical polynomial which is at most finitely renormalizable and has only repelling periodic points is combinatorially rigid. It implies t…
Smoothness of solenoidal attractors
Artur Avila, Sebastien Gouezel, Masato Tsujii
We consider dynamical systems generated by skew products of affine contractions on the real line over angle-multiplying maps on the circle : $ T:S^{1}\times \R\to S^1\times \R…
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…
Examples of Feigenbaum Julia sets with small Hausdorff dimension
Artur Avila, Mikhail Lyubich
We give examples of infinitely renormalizable quadratic polynomials $F_c: z\maps to z^2+c$ with stationary combinatorics whose Julia sets have Hausdorff dimension arbitrar y close…
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…
Bifurcations of unimodal maps
Artur Avila, Carlos Gustavo Moreira
We review recent results that lead to a very precise understanding of the dynamics of typical unimodal maps from the statistical point of view. We also describe the (generalized) r…