Please use this identifier to cite or link to this item: http://hdl.handle.net/10216/94371
Author(s): Alberto A. Pinto
David A. Rand
Title: Solenoid functions for hyperbolic sets on surfaces
Issue Date: 2007
Abstract: We describe a construction of a moduli space of solenoid functionsfor the C1C-conjugacy classes of hyperbolic dynamical systems f onsurfaces with hyperbolic basic sets f . We explain that if the holonomiesare sufficiently smooth then the diffeomorphism f is rigid in the sense that itis C1C conjugate to a hyperbolic affine model. We present a moduli spaceof measure solenoid functions for all Lipschitz conjugacy classes of C1C-hyperbolic dynamical systems f which have a invariant measure that is absolutelycontinuous with respect to Hausdorff measure. We extend Livˇsic andSinai's eigenvalue formula for Anosov diffeomorphisms which preserve an absolutelycontinuousmeasure to hyperbolic basic sets on surfaces which possessan invariant measure absolutely continuous with respect to Hausdorff measure.
Description: We describe a construction of a moduli space of solenoid functionsfor the C1C-conjugacy classes of hyperbolic dynamical systems f onsurfaces with hyperbolic basic sets f . We explain that if the holonomiesare sufficiently smooth then the diffeomorphism f is rigid in the sense that itis C1C conjugate to a hyperbolic affine model. We present a moduli spaceof measure solenoid functions for all Lipschitz conjugacy classes of C1C-hyperbolic dynamical systems f which have a invariant measure that is absolutelycontinuous with respect to Hausdorff measure. We extend Livˇsic andSinai's eigenvalue formula for Anosov diffeomorphisms which preserve an absolutelycontinuousmeasure to hyperbolic basic sets on surfaces which possessan invariant measure absolutely continuous with respect to Hausdorff measure.
Subject: Matemática
Mathematics
URI: http://hdl.handle.net/10216/94371
Source: Dynamics, Ergodic Theory, and Geometry
Document Type: Capítulo ou Parte de Livro
Rights: restrictedAccess
Appears in Collections:FCUP - Capítulo ou Parte de Livro

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