Bifurcations of polynomial functions with diffeomorphic fibers

Francisco Braun; Filipe Fernandes

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arXiv · 2508.01104

Bifurcations of polynomial functions with diffeomorphic fibers

Francisco Braun·Filipe Fernandes

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Abstract

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.

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BibTeX RIS

Francisco Braun, Filipe Fernandes. 2025-08-01. Bifurcations of polynomial functions with diffeomorphic fibers. https://arxiv.org/abs/2508.01104

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