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Decay of correlations for some non-uniformly hyperbolic attractors.
- Source :
- Discrete & Continuous Dynamical Systems: Series A; Mar2024, Vol. 44 Issue 3, p1-20, 20p
- Publication Year :
- 2024
-
Abstract
- We study the decay of correlations for certain dynamical systems with non-uniformly hyperbolic attractors, which natural invariant measure is the Sinai-Ruelle-Bowen (SRB) measure. The system $ g $ that we consider is produced by applying the slow-down procedure to a uniformly hyperbolic diffeomorphism $ f $ with an attractor. Under certain assumptions on the map $ f $ and the slow-down neighborhood, we show that the map $ g $ admits polynomial upper and lower bounds on correlations with respect to its SRB measure and the class of Hölder continuous observables. Our results apply to the Smale-Williams solenoid, as well as its sufficiently small perturbations. [ABSTRACT FROM AUTHOR]
- Subjects :
- HOLDER spaces
INVARIANT measures
DYNAMICAL systems
SOLENOIDS
Subjects
Details
- Language :
- English
- ISSN :
- 10780947
- Volume :
- 44
- Issue :
- 3
- Database :
- Complementary Index
- Journal :
- Discrete & Continuous Dynamical Systems: Series A
- Publication Type :
- Academic Journal
- Accession number :
- 175119850
- Full Text :
- https://doi.org/10.3934/dcds.2023128