On the cyclicity of persistent hyperbolic polycycles

2025/04/09 by Arakaki, Lucas Queiroz, Santana, Paulo · 1 citation
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2504.07225

Abstract

In this work we consider families of smooth vector fields having a persistent polycycle with n hyperbolic saddles. We derive the asymptotic expansion of the return map associated to the polycycle, determining explicitly its leading terms. As a consequence, explicit conditions on the leading terms allow us to determine the cyclicity of such polycycles. We then apply our results to study the cyclicity of a polycycle of a model with applications in Game Theory.

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