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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.09108 |
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| _version_ | 1866910697396371456 |
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| author | Rousseau, Christiane |
| author_facet | Rousseau, Christiane |
| contents | The paper studies the generic complex 1-dimensional polynomial vector fields of the form $iP(z)\frac{\partial}{\partial z}$, where $P$ is a polynomial with real coefficients, under topological orbital equivalence preserving the separatrices of the pole at infinity. The number of generic strata is determined, and a complete parametrization of the strata is given in terms of a modulus formed by a combinatorial part and an analytic part. The bifurcation diagram is described for degrees 3 and 4. A realization theorem is proved for any generic modulus. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_09108 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generic reversible complex polynomial vector fields Rousseau, Christiane Dynamical Systems The paper studies the generic complex 1-dimensional polynomial vector fields of the form $iP(z)\frac{\partial}{\partial z}$, where $P$ is a polynomial with real coefficients, under topological orbital equivalence preserving the separatrices of the pole at infinity. The number of generic strata is determined, and a complete parametrization of the strata is given in terms of a modulus formed by a combinatorial part and an analytic part. The bifurcation diagram is described for degrees 3 and 4. A realization theorem is proved for any generic modulus. |
| title | Generic reversible complex polynomial vector fields |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2411.09108 |