Family of piecewise expanding maps having singular measure as a limit of ACIMs

DOI10.1017/S0143385711000836zbMath1280.37035OpenAlexW2080823390MaRDI QIDQ4911067

Peyman Eslami, Zhenyang Li, Harald Proppe, Góra, Paweł, Boyarski, Abraham

Publication date: 13 March 2013

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0143385711000836

zbMATH Keywords

absolutely continuous invariant measurepiecewise linear mapsingular measureinvariant density

Mathematics Subject Classification ID

Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Dynamical systems involving maps of the interval (37E05) Dynamical systems involving one-parameter continuous families of measure-preserving transformations (37A10)

Related Items (8)

Piecewise convex deterministic dynamical systems and weakly convex random dynamical systems and their invariant measures ⋮ Harmonic averages and new explicit constants for invariant densities of piecewise expanding maps of the interval ⋮ Free Energy and Equilibrium States for Families of Interval Maps ⋮ Harmonic average of slopes and the stability of absolutely continuous invariant measure ⋮ Toward a mathematical holographic principle ⋮ Invariant densities for random systems of the interval ⋮ W-LIKE MAPS WITH VARIOUS INSTABILITIES OF ACIM'S ⋮ Stronger Lasota-Yorke inequality for one-dimensional piecewise expanding transformations

Cites Work

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• Absolutely continuous invariant measures for piecewise expanding \(C^ 2\) transformations in \(\mathbb R^N\)
• Stochastic stability in some chaotic dynamical systems
• Approximating invariant densities of metastable systems
• Invariant densities for piecewise linear maps of the unit interval
• On the isolated spectrum of the Perron-Frobenius operator
• Alternative proofs of linear response for piecewise expanding unimodal maps

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