A dichotomy for higher dimensional flows

2011/10/17 by Alexander Arbieto, A. Arbieto, Arbieto, A. +2
Mathematics · Physics and Astronomy · #37D30 (Primary) 37C10 (Secondary) #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #math.DS #msc:37C10 #msc:37D30

paper · pdf · doi:10.48550/arxiv.1110.3720

10 pages

arxiv created 2011/10/17 · openalex publication_date 2011/10/17 · arxiv updated 2011/10/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We analyze the dichotomy between \em sectional-Axiom A flows (c.f. \citememo) and flows with points accumulated by periodic orbits of different indices. Indeed, this is proved for C¹ generic flows whose singularities accumulated by periodic orbits have codimension one. Our result improves \citemp1.

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