Homoclinic orbits and entropy for three-dimensional flows

2015/09/25 by A. M. Lopez, A. M. López, R. J. Metzger +5
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Primary 37D25 #Quantum chaos and dynamical systems #Secondary 37C40 #math.DS #msc:37C40 #msc:37D25

paper · pdf · doi:10.48550/arxiv.1509.07770

5 pages

arxiv created 2015/09/25 · openalex publication_date 2015/09/25 · arxiv updated 2015/09/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that every C¹ three-dimensional flow with positive topological entropy can be C¹ approximated by flows with homoclinic orbits. This extends a previous result for C¹ surface diffeomorphisms \citeg.

Citations

• Morse-Smale systems and horseshoes for three dimensional singular flows

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