Doubling bifurcations of invariant closed curves in 3D maps
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909791249498112 |
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| author | Biswas, Sayanho Banerjee, Soumitro Avrutin, Viktor Sushko, Iryna |
| author_facet | Biswas, Sayanho Banerjee, Soumitro Avrutin, Viktor Sushko, Iryna |
| contents | Numerous studies have reported two types of doubling of invariant closed curves (ICCs) in dynamical systems: (a) the creation of two disjoint ICCs such that iterations flip between them; and (b) the creation of a single ICC of double the length of the original ICC. Various methods have been proposed to analyze such bifurcations. We show that the methods proposed so far are not always adequate for analyzing and predicting these bifurcations. We propose a new method to overcome the difficulties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_12943 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Doubling bifurcations of invariant closed curves in 3D maps Biswas, Sayanho Banerjee, Soumitro Avrutin, Viktor Sushko, Iryna Dynamical Systems Numerous studies have reported two types of doubling of invariant closed curves (ICCs) in dynamical systems: (a) the creation of two disjoint ICCs such that iterations flip between them; and (b) the creation of a single ICC of double the length of the original ICC. Various methods have been proposed to analyze such bifurcations. We show that the methods proposed so far are not always adequate for analyzing and predicting these bifurcations. We propose a new method to overcome the difficulties. |
| title | Doubling bifurcations of invariant closed curves in 3D maps |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2509.12943 |