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arXiv · 2504.07225

On the cyclicity of persistent hyperbolic polycycles

Lucas Queiroz Arakaki·Paulo Santana
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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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Lucas Queiroz Arakaki, Paulo Santana. 2025-04-09. On the cyclicity of persistent hyperbolic polycycles. https://doi.org/10.1007/s10884-025-10469-9

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