From rates of mixing to recurrence times via large deviations

• Type: Article in International Scientific Journal
• Date: 2011

Authors

alves, jf (Author) FCUP; freitas, jm (Author) FCUP; luzzatto, s (Author) Other; vaienti, s (Author) Other

Journal

Title: Advances in Mathematics

Vol. 228 No. 2

Pages: 1203-1236

ISSN: 0001-8708

Publisher: Elsevier

Indexing

ISI Web of Knowledge - 36 Citations

ISI Web of Science

Scopus - 41 Citations

Scientific classification

FOS: Natural sciences > Mathematics

CORDIS: Physical sciences > Mathematics > Chaos theory

Other information

Authenticus ID: P-002-MBV

DOI: 10.1016/j.aim.2011.06.014

Abstract (EN): A classic approach in dynamical systems is to use particular geometric structures to deduce statistical properties, for example the existence of invariant measures with stochastic-like behaviour such as large deviations or decay of correlations. Such geometric structures are generally highly non-trivial and thus a natural question is the extent to which this approach can be applied. In this paper we show that in many cases stochastic-like behaviour itself implies that the system has certain non-trivial geometric properties, which are therefore necessary as well as sufficient conditions for the occurrence of the statistical properties under consideration. As a by product of our techniques we also obtain some new results on large deviations for certain classes of systems which include Viana maps and multidimensional piecewise expanding maps.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 34