Rational Limit Cycles of Abel Differential Equations

We study the number of rational limit cycles of the Abel equation $x'=A(t)x^3+B(t)x^2$, where $A(t)$ and $B(t)$ are real trigonometric polynomials. We show that this number is at most the degree of $A(t)$ plus one.

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Bibliographische Detailangaben
Hauptverfasser:	Trinidad, José Luis Bravo, Pérez, Luis Ángel Calderón, de Castilla, Ignacio Ojeda Martínez
Format:	Artikel
Sprache:	eng
Schlagworte:	Mathematics - Classical Analysis and ODEs
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Beschreibung
Zusammenfassung:	We study the number of rational limit cycles of the Abel equation $x'=A(t)x^3+B(t)x^2$, where $A(t)$ and $B(t)$ are real trigonometric polynomials. We show that this number is at most the degree of $A(t)$ plus one.
DOI:	10.48550/arxiv.2302.10743