Saved in:
Bibliographic Details
Main Authors: Arakaki, Lucas Queiroz, Santana, Paulo
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2504.07225
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866917143353753600
author Arakaki, Lucas Queiroz
Santana, Paulo
author_facet Arakaki, Lucas Queiroz
Santana, Paulo
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2504_07225
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle On the cyclicity of persistent hyperbolic polycycles
Arakaki, Lucas Queiroz
Santana, Paulo
Dynamical Systems
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.
title On the cyclicity of persistent hyperbolic polycycles
topic Dynamical Systems
url https://arxiv.org/abs/2504.07225