Statistical stability and limit laws for Rovella maps

• Type: Article in International Scientific Journal
• Date: 2012

Authors

alves, jf (Author) FCUP; soufi, m (Author) Other

Journal

Title: Nonlinearity

Vol. 25

Pages: 3527-3552

ISSN: 0951-7715

Publisher: Institute of Physics Publishing

Indexing

ISI Web of Knowledge - 8 Citations

Scopus - 9 Citations

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-002-34Q

DOI: 10.1088/0951-7715/25/12/3527

Abstract (EN): We consider a family of one-dimensional maps arising from the contracting Lorenz attractors studied by Rovella. Benedicks-Carleson techniques were used by Rovella to prove that there is a one-parameter family of maps whose derivatives along their critical orbits increase exponentially fast and the critical orbits have slow recurrence to the critical point. Metzeger proved that these maps have a unique absolutely continuous ergodic invariant probability measure (SRB measure). Here we use the technique developed by Freitas and show that the tail set (the set of points which at a given time have not achieved either the exponential growth of derivative or the slow recurrence) decays exponentially fast as time passes. As a consequence, we obtain the continuous variation (in the L-1-norm) of the densities of the SRB measures and associated metric entropies with the parameter. Our main result also implies some statistical properties for these maps.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 26