Computable conditions for the occurrence of non-uniform hyperbolicity in families of one-dimensional maps

Stefano Luzzatto, Hiroki Takahasi

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

We formulate and prove a Jakobson-Benedicks-Carleson-type theorem on the occurrence of non-uniform hyperbolicity (stochastic dynamics) in families of one-dimensional maps, based on computable starting conditions and providing explicit, computable, lower bounds for the measure of the set of selected parameters. As a first application of our results we show that the set of parameters corresponding to maps in the quadratic family fa(x) ≤ x2 - a which have an absolutely continuous invariant probability measure is at least 10-5000.

Original languageEnglish
Article number013
Pages (from-to)1657-1695
Number of pages39
JournalNonlinearity
Volume19
Issue number7
DOIs
Publication statusPublished - 2006 Jul 1
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

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