Statistical Properties of Unimodal Maps: the Quadratic Family
نویسندگان
چکیده
We prove that almost every non-regular real quadratic map is Collet-Eckmann and has polynomial recurrence of the critical orbit (proving a conjecture by Sinai). It follows that typical quadratic maps have excellent ergodic properties, as exponential decay of correlations (Keller and Nowicki, Young) and stochastic stability in the strong sense (Baladi and Viana). This is an important step to get the same results for more general families of unimodal maps.
منابع مشابه
Statistical Properties of Unimodal Maps: the Quadratic Family Artur Avila and Carlos Gustavo Moreira
We prove that almost every real quadratic map is either regular or Collet-Eckmann with polynomial recurrence of the critical orbit. It follows that typical quadratic maps have excellent ergodic properties, as exponential decay of correlations (Keller and Nowicki, Young) and stochastic stability in the strong sense (Baladi and Viana). This is an important step to get the same results for more ge...
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