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Quantitative statistical stability for equilibrium states of piecewise partially hyperbolic maps.
- Source :
- Discrete & Continuous Dynamical Systems: Series A; Mar2024, Vol. 44 Issue 3, p1-27, 27p
- Publication Year :
- 2024
-
Abstract
- We consider a class of endomorphisms that contains a set of piecewise partially hyperbolic dynamics semi-conjugated to non-uniformly expanding maps. Our goal is to study a class of endomorphisms that preserve a foliation that is almost everywhere uniformly contracted, with possible discontinuity sets parallel to the contracting direction. We apply the spectral gap property and the $ \zeta $-Hölder regularity of the disintegration of its equilibrium states to prove a quantitative statistical stability statement. More precisely, under deterministic perturbations of the system of size $ \delta $, we show that the $ F $-invariant measure varies continuously with respect to a suitable anisotropic norm. Furthermore, we establish that certain interesting classes of perturbations exhibit a modulus of continuity estimated by $ D_2\delta^\zeta \log \delta $, where $ D_2 $ is a constant. [ABSTRACT FROM AUTHOR]
- Subjects :
- STATISTICAL equilibrium
FOLIATIONS (Mathematics)
ENDOMORPHISMS
EQUILIBRIUM
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 :
- 175119857
- Full Text :
- https://doi.org/10.3934/dcds.2023129