Statistical properties of unimodal maps: the quadratic family

• Autores: Carlos Gustavo T. de Moreira, Artur Avila
• Localización: Annals of mathematics, ISSN 0003-486X, Vol. 161, Nº 2, 2005, págs. 831-881
• Idioma: inglés
• DOI: 10.4007/annals.2005.161.831
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• Resumen

  • We prove that almost every nonregular 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 in achieving the same results for more general families of unimodal maps.