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Statistical stability and limit laws for Rovella maps

Title
Statistical stability and limit laws for Rovella maps
Type
Article in International Scientific Journal
Year
2012
Authors
soufi, m
(Author)
Other
The person does not belong to the institution. The person does not belong to the institution. The person does not belong to the institution. Without AUTHENTICUS Without ORCID
Journal
Title: NonlinearityImported from Authenticus Search for Journal Publications
Vol. 25
Pages: 3527-3552
ISSN: 0951-7715
Scientific classification
FOS: Natural sciences > Mathematics
Other information
Authenticus ID: P-002-34Q
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
Contact: jfalves@fc.up.pt; msoufin@gmail.com
No. of pages: 26
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