On the nonexistence of fat partially hyperbolic horseshoes

2005/07/01 by José F. Alves, Alves, José F., Vilton Pinheiro +1
Mathematics · #Advanced Differential Equations and Dynamical Systems #History and Theory of Mathematics #Mathematical Dynamics and Fractals #math.DS #msc:37D30

paper · pdf · doi:10.48550/arxiv.math/0507027

10 pages

arxiv created 2005/07/01 · arxiv updated 2009/12/01

Abstract

We show that there are no partially hyperbolic horseshoes with positive Lebesgue measure for diffeomorphisms whose class of differentiability is higher than 1. This generalizes a classical result by Bowen for uniformly hyperbolic horseshoes.

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