Equivariant hyperbolic diffeomorphisms and representation coverings

2013/07/01 by Hitoshi Yamanaka, Yamanaka, Hitoshi
Mathematics · #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Mathematical Dynamics and Fractals

paper · doi:10.48550/arxiv.1307.0333

openalex publication_date 2013/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a compact Lie group and X be a compact smooth G-manifold with finitely many G-fixed points. We show that if X admits a G-equivariant hyperbolic diffeomorphism having a certain convergence property, there exists an open covering of X indexed by the G-fixed points so that each open set is G-stable and G-equivariantly diffeomorphic to the tangential G-representation at the corresponding G-fixed point. We also show that the converse is also true in case of holomorphic torus actions

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