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math.DS2001
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…
math.DS2001
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…