Using Erdős's methods to study Yorke's problems
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912576595558400 |
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| author | Igra, Eran Sopin, Valerii |
| author_facet | Igra, Eran Sopin, Valerii |
| contents | In this paper, we study the possible bifurcations of periodic orbits by reducing them to graphs. The aforementioned allows to study the genericity of routes to chaos, as well as to analyze their possible complexity. In particular, our results show that there is no upper bound on the possible complexity. Moreover, it suggests general fermionic description via the virial expansion and universal description via the Rado graph. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_06852 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Using Erdős's methods to study Yorke's problems Igra, Eran Sopin, Valerii Dynamical Systems Classical Analysis and ODEs Combinatorics 37E15, 37B30, 37G15, 05C90, 05C05 In this paper, we study the possible bifurcations of periodic orbits by reducing them to graphs. The aforementioned allows to study the genericity of routes to chaos, as well as to analyze their possible complexity. In particular, our results show that there is no upper bound on the possible complexity. Moreover, it suggests general fermionic description via the virial expansion and universal description via the Rado graph. |
| title | Using Erdős's methods to study Yorke's problems |
| topic | Dynamical Systems Classical Analysis and ODEs Combinatorics 37E15, 37B30, 37G15, 05C90, 05C05 |
| url | https://arxiv.org/abs/2509.06852 |