Stable sets of certain non-uniformly hyperbolic horseshoes have the\n expected dimension

2017/12/18 by Carlos Matheus, Matheus, Carlos, Jacob Palis +3
Mathematics · #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1712.06629

openalex publication_date 2017/12/18 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

We show that the stable and unstable sets of non-uniformly hyperbolic\nhorseshoes arising in some heteroclinic bifurcations of surface diffeomorphisms\nhave the value conjectured in a previous work by the second and third authors\nof the present paper. Our results apply to first heteroclinic bifurcations\nassociated to horseshoes with Hausdorff dimension <22/21 of conservative\nsurface diffeomorphisms.\n

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