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

Stefano Luzzatto; Hiroki Takahasi

doi:10.1088/0951-7715/19/7/013

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

Stefano Luzzatto, Hiroki Takahasi

Research output: Contribution to journal › Article › peer-review

13 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 f_a(x) ≤ x² - a which have an absolutely continuous invariant probability measure is at least 10^-5000.

Original language	English
Article number	013
Pages (from-to)	1657-1695
Number of pages	39
Journal	Nonlinearity
Volume	19
Issue number	7
DOIs	https://doi.org/10.1088/0951-7715/19/7/013
Publication status	Published - 2006 Jul 1
Externally published	Yes

ASJC Scopus subject areas

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

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10.1088/0951-7715/19/7/013

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

Abstract

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