Multiplicity of limit cycles that appear after perturbations of hyperbolic polycycles

2022/01/10 by Andrei Dukov, Dukov, Andrei
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Quantum chaos and dynamical systems #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2201.03652

Abstract

We consider the multiplicity of limit cycles that appear when a hyperbolic polycycle is perturbed. We prove, in particular, that if such unfolding happens in generic finite-parameter families, the multiplicity of every new limit cycle does not exceed the number of separatrix connections in the polycycle.

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