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Modulus of continuity of invariant densities and entropies for piecewise expanding maps

Part of: Ergodic theory Smooth dynamical systems: general theory

Published online by Cambridge University Press:  07 April 2025

JOSÉ F. ALVES Open the ORCID record for JOSÉ F. ALVES [Opens in a new window]  and
ODAUDU ETUBI Open the ORCID record for ODAUDU ETUBI [Opens in a new window]
JOSÉ F. ALVES*
Affiliation:
Centro de Matemática da Universidade do Porto, Rua do Campo Alegre 687, Porto 4169-007, Portugal (e-mail: etubiodaudu@gmail.com)
ODAUDU ETUBI
Affiliation:
Centro de Matemática da Universidade do Porto, Rua do Campo Alegre 687, Porto 4169-007, Portugal (e-mail: etubiodaudu@gmail.com)
*
e-mail: jfalves@fc.up.pt
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Abstract

Using a perturbation result established by Galatolo and Lucena [Spectral gap and quantitative statistical stability for systems with contracting fibers and Lorenz-like maps. Discrete Contin. Dyn. Syst. 40(3) (2020), 1309–1360], we obtain quantitative estimates on the continuity of the invariant densities and entropies of the physical measures for some families of piecewise expanding maps. We apply these results to a family of two-dimensional tent maps.

Keywords

piecewise expanding mapsmetric entropymodulus of continuity

MSC classification

Primary: 37A05: Measure-preserving transformations 37A10: One-parameter continuous families of measure-preserving transformations 37A35: Entropy and other invariants, isomorphism, classification
Secondary: 37C40: Smooth ergodic theory, invariant measures 37C75: Stability theory

Information

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 45 , Issue 10 , October 2025 , pp. 2976 - 2991
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Copyright
© The Author(s), 2025. Published by Cambridge University Press

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