Periodic orbits for real planar polynomial vector fields of degree n having n invariant straight lines taking into account their multiplicities

Periodic orbits for real planar polynomial vector fields of degree n having n invariant straight lines taking into account their multiplicities

We study the existence and non--existence of periodic orbits and limit cycles for planar polynomial differential systems of degree $n$ having $n$ real invariant straight lines taking into account their multiplicities. The polynomial differential systems with $n=1,2,3$ are completely characterized.

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Veröffentlicht in:Electronic journal of qualitative theory of differential equations 2015-01, Vol.2015 (55), p.1-15
Hauptverfasser: Llibre, Jaume, Rodrigues, Ana Wendell O
Format: Artikel
Sprache:eng
Schlagworte:
invariant straight lines
limit cycles
periodic orbits
polynomial differential systems
polynomial vector fields
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Beschreibung
Zusammenfassung:We study the existence and non--existence of periodic orbits and limit cycles for planar polynomial differential systems of degree $n$ having $n$ real invariant straight lines taking into account their multiplicities. The polynomial differential systems with $n=1,2,3$ are completely characterized.
ISSN:1417-3875
1417-3875
DOI:10.14232/ejqtde.2015.1.55