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GIBBS MEASURES FOR ONE-DIMENSIONAL ATTRACTORS OF HYPERBOLIC MAPPINGS WITH SINGULARITIES

Name: GIBBS MEASURES FOR ONE-DIMENSIONAL ATTRACTORS OF HYPERBOLIC MAPPINGS WITH SINGULARITIES
Creator: Evgueni A Sataev
Keywords: Dynamical systems with hyperbolic behavior, Attractors and repellers of smooth dynamical systems and their topological structure, Ergodic theory, Gibbs measure, 0101 mathematics, Measure-preserving transformations, one-dimensional attractors, singularities, 01 natural sciences, hyperbolic mappings

Gibbs measures for one-dimensional attractors of hyperbolic mappings with singularities

descriptionPublicationkeyboard_double_arrow_right Article 30 Jun 1993Publisher:Steklov Mathematical InstituteJournal:Russian Academy of Sciences. Izvestiya Mathematics, volume 41, pages 567-580 (issn: 1064-5632,

Authors: Evgueni A Sataev;

doi: 10.1070/im1993v041n03abeh002276

GIBBS MEASURES FOR ONE-DIMENSIONAL ATTRACTORS OF HYPERBOLIC MAPPINGS WITH SINGULARITIES

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Abstract

The author constructs and investigates the properties of a \(u\)-Gibbs invariant measure for hyperbolic mappings with singularities, for which the unstable subspace is one-dimensional, and which satisfy some regularity conditions. These conditions are satisfied by the Lorentz mapping, the Lozi mapping and the Belykh mapping among others. Finally there are studied the periodic trajectories, topological transitivity, and the convergence of the means.

Keywords

Dynamical systems with hyperbolic behavior, Attractors and repellers of smooth dynamical systems and their topological structure, Ergodic theory, Gibbs measure, Measure-preserving transformations, one-dimensional attractors, singularities, hyperbolic mappings

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