Topological classification of limit periodic sets of polynomial planar vector fields
| Autor: | José Ginés Espín Buendía, André Belotto da Silva |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Semialgebraic set
Pure mathematics Polynomial General Mathematics 37G15 34C07 34C08 (Primary) 14P10 37G15 (Secondary) Semi-algebraic sets Set (abstract data type) semi-algebraic sets Dimension (vector space) limit periodic sets 34C08 Mathematics - Classical Analysis and ODEs ordinary differential equations 34C07 Ordinary differential equation Limit periodic sets 14P10 Limit (mathematics) Algebraic number Topological conjugacy Ordinary differential equations Mathematics |
| Zdroj: | Publicacions Matemàtiques; Vol. 63, Núm. 1 (2019); p. 105-123 Dipòsit Digital de Documents de la UAB Universitat Autònoma de Barcelona Publ. Mat. 63, no. 1 (2019), 105-123 |
| ISSN: | 0214-1493 |
| Popis: | We characterize the limit periodic sets of families of polynomial planar vector fields up to homeomorphisms. We show that any limit periodic set is topologically equivalent to a compact and connected semialgebraic set of the sphere with empty interior. Conversely, we show that any compact and connected semialgebraic set of the sphere with empty interior can be realized as a limit periodic set. Comment: 15 pages, 3 figures |
| Databáze: | OpenAIRE |
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