93 citations · 950 across the 70 of their papers we have counts for
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Infinitesimal perturbations of rational maps
Artur Avila
We analyze the infinitesimal effect of holomorphic perturbations of the dynamics of a structurally stable rational map on a neighborhood of its Julia set. This implies some restric…
Quasisymmetric robustness of the Collet-Eckmann condition in the quadratic family
Artur Avila, Carlos Gustavo Moreira
We consider quasisymmetric reparametrizations of the parameter space of the quadratic family. We prove that the set of quadratic maps which are either regular or Collet-Eckmann wit…
Statistical properties of unimodal maps: smooth families with negative Schwarzian derivative
Artur Avila, Carlos Gustavo Moreira
We prove that there is a residual set of families of smooth or analytic unimodal maps with quadratic critical point and negative Schwarzian derivative such that almost every non-re…
A formula with some applications to the theory of Lyapunov exponents
Artur Avila, Jairo Bochi
We prove an elementary formula about the average expansion of certain products of 2 by 2 matrices. This permits us to quickly re-obtain an inequality by M. Herman and a theorem by…