Topological entropy of Lorenz-like flows

2014/12/03 by Jiagang Yang, Yang, Jiagang · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #37A35 #37B40 #37C10 #37D25 #37D30 #37D50 #Chaos control and synchronization #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Nonlinear Dynamics and Pattern Formation #math.DS #msc:37A35 #msc:37B40 #msc:37C10 #msc:37D25 #msc:37D30 #msc:37D50

paper · pdf · doi:10.48550/arxiv.1412.1207

arxiv created 2014/12/03 · openalex publication_date 2014/12/03 · arxiv updated 2014/12/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We use entropy theory as a new tool for studying Lorenz-like classes of flows in any dimension. More precisely, we show that every Lorenz-like class is entropy expansive, and has positive entropy which varies continuously with vector fields. We deduce that every such class contains a transverse homoclinic orbit and, generically, is an attractor.

Citations

• Deterministic Nonperiodic Flow

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