2012/02/03 by B. Alarcon, Begoña Alarcón, Sofia B. S. D. Castro +6 · 1 citation
Mathematics · #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #math.DS
paper · pdf · doi:10.48550/arxiv.1202.0779
openalex publication_date 2012/02/03 · arxiv created 2012/09/17 · arxiv updated 2012/09/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider sufficient conditions to determine the global dynamics for equivariant maps of the plane with a unique fixed point which is also hyperbolic. When the map is equivariant under the action of a compact Lie group, it is possible to describe the local dynamics. In particular, if the group contains a reflection, there is a line invariant by the map. This allows us to use results based on the theory of free homeomorphisms to describe the global dynamical behaviour. We briefly discuss the case when reflections are absent, for which global dynamics may not follow from local dynamics near the unique fixed point.