4 citations · 19 across the 8 of their papers we have counts for
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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★ 4 cited
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…
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…