The Uniform Isochronous Centers with Homogeneous Nonlinearities of Degree 5
The interest in studying the uniform isochronous centers goes back to C. Huygens in the XVII century. Since then, many papers have been published on this subject. In particular, the phase portraits of the polynomial uniform isochronous center up to degree four have been classified. In this paper, we...
| Authors: | , |
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| Format: | article |
| Publication Date: | 2025 |
| Country: | España |
| Institution: | Universitat Autònoma de Barcelona |
| Repository: | Dipòsit Digital de Documents de la UAB |
| Language: | English |
| OAI Identifier: | oai:ddd.uab.cat:318292 |
| Online Access: | https://ddd.uab.cat/record/318292 https://dx.doi.org/urn:doi:10.1007/s10883-025-09734-3 |
| Access Level: | Embargoed access |
| Keyword: | Uniform isochronous center Polynomial vector field Phase portrait Separatrix configuration Periodic orbit |
| Summary: | The interest in studying the uniform isochronous centers goes back to C. Huygens in the XVII century. Since then, many papers have been published on this subject. In particular, the phase portraits of the polynomial uniform isochronous center up to degree four have been classified. In this paper, we classify the topological phase portraits of polynomial differential systems with a uniform isochronous center, whose nonlinear part is a homogeneous polynomial of degree 5. We prove that there are three distinct topological phase portraits in the Poincaré disc for such polynomial differential systems. |
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