Global Saddles for Planar Maps

2016/05/25 by Begoña Alarcón, Sofia B. S. D. Castro, Alarcón, Begoña +3
Mathematics · Physics and Astronomy · #37B99 #37C80 #54H20 #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #math.DS #msc:37B99 #msc:37C80 #msc:54H20

paper · pdf · doi:10.48550/arxiv.1605.08000

openalex publication_date 2016/05/25 · arxiv created 2016/09/14 · arxiv updated 2016/09/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the dynamics of planar diffeomorphisms having a unique fixed point that is a hyperbolic local saddle. We obtain sufficient conditions under which the fixed point is a global saddle. We also address the special case of D₂-symmetric maps, for which we obtain a similar result for C¹ homeomorphisms. Some applications to differential equations are also given.

Related

• Global Dynamics for Symmetric Planar Maps
• Discrete Symmetric Planar Dynamics
• A Global Hartman-Grobman Theorem
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• Dynamics of C¹-diffeomorphisms: global description and prospects for classification