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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.07225 |
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| _version_ | 1866917143353753600 |
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| 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 |