No or infinitely many a. c. i. p. for piecewise expanding \(C^r\) maps in higher dimensions

DOI10.1007/s002200100509zbMath1001.37003OpenAlexW2066126788MaRDI QIDQ5959069

Jérôme Buzzi

Publication date: 2 January 2003

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s002200100509

zbMATH Keywords

ergodicityexpandingabsolutely continuous probability measuresrepelling point

Mathematics Subject Classification ID

Dynamical aspects of measure-preserving transformations (37A05) Smooth ergodic theory, invariant measures for smooth dynamical systems (37C40) Low-dimensional dynamical systems (37E99) Dynamical systems with hyperbolic behavior (37D99)

Related Items (14)

SRB measures for higher dimensional singular partially hyperbolic attractors ⋮ A semi-invertible operator Oseledets theorem ⋮ Invariant measures for random expanding on average Saussol maps ⋮ Observable Lyapunov irregular sets for planar piecewise expanding maps ⋮ Positive Lyapunov exponent for random perturbations of predominantly expanding multimodal circle maps ⋮ ENTROPY OF EQUILIBRIUM MEASURES OF CONTINUOUS PIECEWISE MONOTONIC MAPS ⋮ Multidimensional expanding maps with singularities: a pedestrian approach ⋮ Existence, uniqueness and stability of equilibrium states for non-uniformly expanding maps ⋮ Invariant measures with bounded variation densities for piecewise area preserving maps ⋮ Good Banach spaces for piecewise hyperbolic maps via interpolation ⋮ Multidimensional hyperbolic billiards ⋮ Detecting isolated spectrum of transfer and Koopman operators with Fourier analytic tools ⋮ On the number of invariant measures for random expanding maps in higher dimensions ⋮ Decay of correlations for piecewise invertible maps in higher dimensions

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