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- Title
Quantitative statistical stability for equilibrium states of piecewise partially hyperbolic maps.
- Authors
Bilbao, Rafael; Bioni, Ricardo; Lucena, Rafael
- 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.
- Subjects
STATISTICAL equilibrium; FOLIATIONS (Mathematics); ENDOMORPHISMS; EQUILIBRIUM
- Publication
Discrete & Continuous Dynamical Systems: Series A, 2024, Vol 44, Issue 3, p1
- ISSN
1078-0947
- Publication type
Article
- DOI
10.3934/dcds.2023129