Normal forms and global phase portraits of quadratic and cubic integrable vector fields having two nonconcentric circles as invariant algebraic curves
In this paper, we give the normal form of all planar polynomial vector fields of degree d ≤ 3 having two nonconcentric circles C1 and C2 as invariant algebraic curves and the function H=Cβ 1 Cα 2, with α and β real values, as first integral. Moreover, we classify all global phase portraits on the Po...
| Authors: | , , |
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| Format: | article |
| Status: | Published version |
| Publication Date: | 2017 |
| Country: | Brasil |
| Institution: | Universidade Estadual Paulista (UNESP) |
| Repository: | Repositório Institucional da UNESP |
| Language: | English |
| OAI Identifier: | oai:repositorio.unesp.br:11449/173924 |
| Online Access: | http://dx.doi.org/10.1080/14689367.2016.1263600 http://hdl.handle.net/11449/173924 |
| Access Level: | Open access |
| Keyword: | global analysis invariant algebraic curves limit cycles normal forms Poincaré compactification Quadratic and cubic vector fields |
| Summary: | In this paper, we give the normal form of all planar polynomial vector fields of degree d ≤ 3 having two nonconcentric circles C1 and C2 as invariant algebraic curves and the function H=Cβ 1 Cα 2, with α and β real values, as first integral. Moreover, we classify all global phase portraits on the Poincaré disc of a subclass of these vector fields. |
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