Minimal Diffeomorphisms cannot satisfy Generalized Dominated Splitting

2011/06/19 by Xueting Tian, Tian, Xueting
Mathematics · Physics and Astronomy · #37B20 #37C40 #37D30 #Advanced Differential Equations and Dynamical Systems #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Dynamics and Fractals #Mathematical Physics (math-ph) #math-ph #math.DS #math.MP #msc:37B20 #msc:37C40 #msc:37D30

paper · pdf · doi:10.48550/arxiv.1106.3737

9pages, 1 figures

arxiv created 2011/06/19 · openalex publication_date 2011/06/19 · arxiv updated 2011/06/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce a new notion called generalized dominated splitting which is weaker than classical dominated splitting. We use this notion to generalize a result of Zhang\citeZh: every diffeomorphism with nontrivial global generalized dominated splitting can not be minimal.

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