Rational Limit Cycles on Abel Polynomial Equations

Claudia Valls
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Claudia Valls: Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, Portugal

Mathematics, 2020, vol. 8, issue 6, 1-15

Abstract: In this paper we deal with Abel equations of the form d y / d x = A 1 ( x ) y + A 2 ( x ) y 2 + A 3 ( x ) y 3 , where A 1 ( x ) , A 2 ( x ) and A 3 ( x ) are real polynomials and A 3 ? 0 . We prove that these Abel equations can have at most two rational (non-polynomial) limit cycles when A 1 ? 0 and three rational (non-polynomial) limit cycles when A 1 ≡ 0 . Moreover, we show that these upper bounds are sharp. We show that the general Abel equations can always be reduced to this one.

Keywords: algebraic limit cycles; rational limit cycles; abel equations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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