A Hölder continuous vector field tangent to many foliations

2003/03/24 by Christian Bonatti, John Franks, Bonatti, Christian +1 · 1 citation
Mathematics · #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals #math.DS

paper · pdf · doi:10.48550/arxiv.math/0303291

arxiv created 2003/03/24 · openalex publication_date 2003/03/24 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct an example of a Hölder continuous vector field on the plane which is tangent to all foliations in a continuous family of pairwise distinct C¹ foliations. Given any 1 ≤ r

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