Qualitative planar dynamics with star nodes and homogeneous nonlinearities: beyond Hilbert's $16^{th}$ problem
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2021
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| _version_ | 1866912886055501824 |
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| author | Alarcón, Begoña Castro, Sofia B. S. D. Labouriau, Isabel S. |
| author_facet | Alarcón, Begoña Castro, Sofia B. S. D. Labouriau, Isabel S. |
| contents | This is a full study of the dynamics of polynomial planar vector fields whose linear part is a multiple of the identity and whose nonlinear part is a homogeneous polynomial of arbitrary degree $n>1$. It extends previous work by other authors that was mainly concerned with the existence and number of limit cycles. The general results are also applied to two classes of examples where the nonlinearities have degrees 2 and 3, for which we provide a set of phase portraits. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2106_07516 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Qualitative planar dynamics with star nodes and homogeneous nonlinearities: beyond Hilbert's $16^{th}$ problem Alarcón, Begoña Castro, Sofia B. S. D. Labouriau, Isabel S. Dynamical Systems 34C05 This is a full study of the dynamics of polynomial planar vector fields whose linear part is a multiple of the identity and whose nonlinear part is a homogeneous polynomial of arbitrary degree $n>1$. It extends previous work by other authors that was mainly concerned with the existence and number of limit cycles. The general results are also applied to two classes of examples where the nonlinearities have degrees 2 and 3, for which we provide a set of phase portraits. |
| title | Qualitative planar dynamics with star nodes and homogeneous nonlinearities: beyond Hilbert's $16^{th}$ problem |
| topic | Dynamical Systems 34C05 |
| url | https://arxiv.org/abs/2106.07516 |