Limit cycles and Lie symmetries
Visualitza/Obre
Estadístiques de LA Referencia / Recolecta
Inclou dades d'ús des de 2022
Cita com:
hdl:2117/943
Tipus de documentArticle
Data publicació2005
Condicions d'accésAccés obert
Llevat que s'hi indiqui el contrari, els
continguts d'aquesta obra estan subjectes a la llicència de Creative Commons
:
Reconeixement-NoComercial-SenseObraDerivada 2.5 Espanya
Abstract
Given a planar vector field U which generates the Lie symmetry of some other
vector field X, we prove a new criterion to control the stability of the periodic orbits
of U. The problem is linked to a classical problem proposed by A.T. Winfree in the
seventies about the existence of isochrons of limit cycles (the question suggested by
the study of biological clocks), already answered by Guckenheimer using a different
terminology. We apply our criterion to give upper bounds of the number of limit cycles
for some families of vector fields as well as to provide a class of vector fields with a
prescribed number of hyperbolic limit cycles. Finally we show how this procedure
solves the problem of the hyperbolicity of periodic orbits in problems where other
criteria, like the classical one of the divergence, fail.
Fitxers | Descripció | Mida | Format | Visualitza |
---|---|---|---|---|
050601guillamon.pdf | 253,4Kb | Visualitza/Obre |