ABSOLUTELY CONTINUOUS INVARIANT MEASURES FOR GENERIC MULTI-DIMENSIONAL PIECEWISE AFFINE EXPANDING MAPS

DOI10.1142/S021812749900122XzbMath1089.37513OpenAlexW2143841218MaRDI QIDQ5474024

Jérôme Buzzi

Publication date: 23 June 2006

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s021812749900122x

Mathematics Subject Classification ID

Measure-preserving transformations (28D05) Dynamical aspects of measure-preserving transformations (37A05) Smooth ergodic theory, invariant measures for smooth dynamical systems (37C40) Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20)

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Cites Work

• Absolutely continuous invariant measures for piecewise expanding \(C^ 2\) transformations in \(\mathbb R^N\)
• Lyapunov exponents, entropy and periodic orbits for diffeomorphisms
• Intrinsic ergodicity of affine maps in \([0,1^ d\)]
• An inequality for the entropy of differentiable maps
• Absolutely continuous invariant measures for piecewise expanding C² transformations in Rⁿ on domains with cusps on the boundaries