Lyapunov exponents and rates of mixing for one-dimensional maps

• Type: Article in International Scientific Journal
• Date: 2004

Authors

alves, jf (Author) FCUP; luzzatto, s (Author) Other; pinheiro, v (Author) Other

Journal

Title: Ergodic Theory and Dynamical Systems

Vol. 24

Pages: 637-657

ISSN: 0143-3857

Publisher: Cambridge University Press

Indexing

ISI Web of Knowledge - 26 Citations

Scopus - 27 Citations

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-000-A2N

DOI: 10.1017/s0143385703000579

Abstract (EN): We show that one-dimensional maps f with strictly positive Lyapunov exponents almost everywhere admit an absolutely continuous invariant measure. If f is topologically transitive, some power of f is mixing and, in particular, the correlation of Holder continuous observables decays to zero. The main objective of this paper is to show that the rate of decay of correlations is determined, in some situations, by the average rate at which typical points start to exhibit exponential growth of the derivative.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 21