Rational limit cycles of Abel equations
In this paper we deal with Abel equations dy/dx = A(x)y2 + B(x)y3, where A(x) and B(x) are real polynomials. We prove that these Abel equations can have at most three rational limit cycles and we characterize when this happens. Moreover, we provide examples of these Abel equations with three nontriv...
| Authors: | , |
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| Format: | article |
| Publication Date: | 2021 |
| Country: | España |
| Institution: | Universitat Autònoma de Barcelona |
| Repository: | Dipòsit Digital de Documents de la UAB |
| Language: | English |
| OAI Identifier: | oai:ddd.uab.cat:239782 |
| Online Access: | https://ddd.uab.cat/record/239782 https://dx.doi.org/urn:doi:10.3934/CPAA.2021007 |
| Access Level: | Open access |
| Keyword: | Algebraic limit cycles Rational limit cycles Abel equations Hyperbolic limit cycles |
| Summary: | In this paper we deal with Abel equations dy/dx = A(x)y2 + B(x)y3, where A(x) and B(x) are real polynomials. We prove that these Abel equations can have at most three rational limit cycles and we characterize when this happens. Moreover, we provide examples of these Abel equations with three nontrivial rational limit cycles. We also prove that in this case the limit cycles cannot be hyperbolic. |
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