Discrete Symmetric Planar Dynamics
B. Alarc\'on, S.B.S.D. Castro, I.S. Labouriau
TL;DR
This paper reviews conditions under which the global dynamics of symmetric planar maps with a single hyperbolic fixed point can be determined, focusing on equivariant maps and their behavior.
Contribution
It synthesizes existing results to clarify how symmetry and hyperbolicity influence the global dynamics of planar maps.
Findings
Provides sufficient conditions for global dynamics determination
Highlights the role of symmetry in planar dynamics
Summarizes key results on hyperbolic fixed points
Abstract
We review previous results providing sufficient conditions to determine the global dynamics for equivariant maps of the plane with a unique fixed point which is also hyperbolic.
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Quantum chaos and dynamical systems · Mathematical Dynamics and Fractals