Collet-Eckmann condition and backward Collet-Eckmann condition for multi-modal maps
نویسندگان
چکیده
منابع مشابه
Quasisymmetric Robustness of the Collet-eckmann Condition in the Quadratic Family
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 with polynomial recurrence of the critical orbit has full Lebesgue measure.
متن کاملAnalyticity of the Srb Measure for Holomorphic Families of Quadratic-like Collet-eckmann Maps
We show that if ft is a holomorphic family of quadratic-like maps with all periodic orbits repelling so that for each real t the map ft is a real Collet-Eckmann S-unimodal map then, writing μt for the unique absolutely continuous invariant probability measure of ft, the map
متن کاملQuasisymmetric Robustness of the Collet-eckmann Condition in the Quadratic Family Artur Avila and 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 with polynomial recurrence of the critical orbit has full Lebesgue measure.
متن کاملA Proof That S-unimodal Maps Are Collet-eckmann Maps in a Specific Range of Their Bifurcation Parameters
Generally, Collet-Eckmann maps require unimodality and multimodality. The inverse is not true. In this paper, we will prove that S-unimodal maps are Collet-Eckmann maps in a specific range of their bifurcation parameters. The proof is based on the fact that the family of robustly chaotic unimodal maps known in the literature are all topologically conjugate to one another and the fact that if tw...
متن کاملStatistical Properties of Unimodal Maps: Smooth Families with Negative Schwarzian Derivative
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-regular parameter is Collet-Eckmann with subexponential recurrence of the critical orbit. Those conditions lead to a detailed and robust statistical description of the dynamics. This proves the Palis conjecture in this ...
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ژورنال
عنوان ژورنال: SCIENTIA SINICA Mathematica
سال: 2016
ISSN: 1674-7216
DOI: 10.1360/n012016-00132