Parabolic bifurcation loci in the spaces of rational functions
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910287121088512 |
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| author | Okuyama, Yûsuke |
| author_facet | Okuyama, Yûsuke |
| contents | We give a geometric description of the parabolic bifurcation locus in the space $\operatorname{Rat}_d$ of all rational functions on $\mathbb{P}^1$ of degree $d>1$, generalizing the study by Morton and Vivaldi in the case of monic polynomials. The results are new even for quadratic rational functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_02005 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Parabolic bifurcation loci in the spaces of rational functions Okuyama, Yûsuke Algebraic Geometry Complex Variables Dynamical Systems Number Theory We give a geometric description of the parabolic bifurcation locus in the space $\operatorname{Rat}_d$ of all rational functions on $\mathbb{P}^1$ of degree $d>1$, generalizing the study by Morton and Vivaldi in the case of monic polynomials. The results are new even for quadratic rational functions. |
| title | Parabolic bifurcation loci in the spaces of rational functions |
| topic | Algebraic Geometry Complex Variables Dynamical Systems Number Theory |
| url | https://arxiv.org/abs/2401.02005 |