Abel quadratic differential systems of second kind
The Abel differential equations of second kind, named after Niels Henrik Abel, are a class of ordinary differential equations studied by many authors. Here we consider the Abel quadratic polynomial differential equations of second kind denoting this class by QSAb. Firstly we split the whole family o...
| Authors: | ; ; ; |
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| Format: | Article |
| Publication date: | 2024 |
| Country: | España |
| Institution: | Universitat Autònoma de Barcelona |
| Repository: | Dipòsit Digital de Documents de la UAB |
| Language: | English |
| OAI Identifier: | oai:ddd.uab.cat:307716 |
| Online Access: | https://ddd.uab.cat/record/307716 https://dx.doi.org/urn:doi:10.58997/ejde.2024.50 |
| Access Level: | Open access |
| Keyword: | Quadratic differential systems Phase portraits Second kind of Abel differential equations Affine invariant polynomials |
| Summary: | The Abel differential equations of second kind, named after Niels Henrik Abel, are a class of ordinary differential equations studied by many authors. Here we consider the Abel quadratic polynomial differential equations of second kind denoting this class by QSAb. Firstly we split the whole family of non-degenerate quadratic systems in four subfamilies according to the number of infinite singularities. Secondly for each one of these four subfamilies we determine necessary and sufficient affine invariant conditions for a quadratic system in this subfamily to belong to the class QSAb. Thirdly we classify all the phase portraits in the Poincaré disc of the systems in QSAb in the case when they have at infinity either one triple singularity (21 phase portraits) or an infinite number of singularities (9 phase portraits). Moreover we determine the affine invariant criteria for the realization of each one of the 30 topologically distinct phase portraits. |
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