Bifurcations of polynomial functions with diffeomorphic fibers
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915422959304704 |
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| author | Braun, Francisco Fernandes, Filipe |
| author_facet | Braun, Francisco Fernandes, Filipe |
| contents | The phenomena that cause a value of a polynomial function to be a bifurcation one are yet to be described when the fibers have dimension higher than $1$. In this note, the main result is the construction of a polynomial submersion function of $\mathbb{R}^3$ with connected fibers having a bifurcation value such that close enough to it the fibers are mutually diffeomorphic. We also present an example of a polynomial submersion function of $\mathbb{R}^2$ having a bifurcation value such that close enough to it the fibers are mutually diffeomorphic. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_01104 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bifurcations of polynomial functions with diffeomorphic fibers Braun, Francisco Fernandes, Filipe Algebraic Geometry Dynamical Systems 14D06, 57R45, 58K05, 32S20 The phenomena that cause a value of a polynomial function to be a bifurcation one are yet to be described when the fibers have dimension higher than $1$. In this note, the main result is the construction of a polynomial submersion function of $\mathbb{R}^3$ with connected fibers having a bifurcation value such that close enough to it the fibers are mutually diffeomorphic. We also present an example of a polynomial submersion function of $\mathbb{R}^2$ having a bifurcation value such that close enough to it the fibers are mutually diffeomorphic. |
| title | Bifurcations of polynomial functions with diffeomorphic fibers |
| topic | Algebraic Geometry Dynamical Systems 14D06, 57R45, 58K05, 32S20 |
| url | https://arxiv.org/abs/2508.01104 |