Polynomial differential systems with explicit non-algebraic limit cycles
Up to know all the examples of polynomial differential systems for which non-algebraic limit cycles are known explicitly have degree ≥ 5. Here we show that already there are polynomial differential systems of degree ≥ 3 exhibiting explicit non-algebraic limit cycles. It is well known that polynomial...
| Autores: | , |
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| Tipo de documento: | artigo |
| Data de publicação: | 2012 |
| País: | España |
| Recursos: | Universitat Autònoma de Barcelona |
| Repositório: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglês |
| OAI Identifier: | oai:ddd.uab.cat:150529 |
| Acesso em linha: | https://ddd.uab.cat/record/150529 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Non-algebraic limit cycle Polynomial vector field |
| Resumo: | Up to know all the examples of polynomial differential systems for which non-algebraic limit cycles are known explicitly have degree ≥ 5. Here we show that already there are polynomial differential systems of degree ≥ 3 exhibiting explicit non-algebraic limit cycles. It is well known that polynomial differential systems of degree 1 (i.e. linear differential systems) has no limit cycles. It remains the open question to determine if the polynomial differential systems of degree 2 can exhibit explicit non-algebraic limit cycles. |
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