Quantitative statistical stability for equilibrium states of piecewise partially hyperbolic maps

DOI10.3934/dcds.2023129arXiv2008.05679MaRDI QIDQ6187260

Rafael A. Bilbao, Ricardo Bioni, Rafael Lucena

Publication date: 15 January 2024

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2008.05679

zbMATH Keywords

stabilityspectral gapequilibrium statesdiscontinuous systemspartially hyperbolic

Mathematics Subject Classification ID

Thermodynamic formalism, variational principles, equilibrium states for dynamical systems (37D35) Partially hyperbolic systems and dominated splittings (37D30) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25)

Cites Work

• Existence, uniqueness and stability of equilibrium states for non-uniformly expanding maps
• Spectral gap and quantitative statistical stability for systems with contracting fibers and Lorenz-like maps
• Equilibrium states for non-uniformly expanding maps: decay of correlations and strong stability
• Statistical properties of the maximal entropy measure for partially hyperbolic attractors
• Lorenz-like flows: exponential decay of correlations for the Poincaré map, logarithm law, quantitative recurrence
• Three-Dimensional Flows
• A Relativised Variational Principle for Continuous Transformations
• Quantitative statistical stability, speed of convergence to equilibrium and partially hyperbolic skew products
• Hölder regularity and exponential decay of correlations for a class of piecewise partially hyperbolic maps

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