Statistical properties of unimodal maps: the quadratic family
نویسندگان
چکیده
منابع مشابه
Statistical Properties of Unimodal Maps: the Quadratic Family
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...
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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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We prove that almost every real quadratic map is either regular or Collet-Eckmann. This implies exponential rates of mixing of the last renormalization of the map. We also show that the recurrence of the critical orbit is polynomial in a full measure set. It follows from a result of Baladi and Viana that almost every quadratic map is stochastically stable in the strong sense. Combined with meth...
متن کاملJa n 20 01 STATISTICAL PROPERTIES OF UNIMODAL MAPS
We prove that almost every real quadratic map is either regular or Collet-Eckmann. This implies exponential rates of mixing of the last renormalization of the map. We also show that the recurrence of the critical orbit is polynomial in a full measure set. It follows from a result of Baladi and Viana that almost every quadratic map is stochastically stable in the strong sense. Combined with meth...
متن کاملPhase-parameter Relation and Sharp Statistical Properties for General Families of Unimodal Maps
We obtain precise estimates relating the phase space and the parameter space of analytic families of unimodal maps, which generalize the case of the quadratic family obtained in [AM1]. This result implies a statistical description of the dynamics of typical analytic quasiquadratic maps which is much sharper than what was previously known: as an example, we can conclude that the recurrence of th...
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ژورنال
عنوان ژورنال: Annals of Mathematics
سال: 2005
ISSN: 0003-486X
DOI: 10.4007/annals.2005.161.831