To access the full text documents, please follow this link: http://hdl.handle.net/2117/943

Limit cycles and Lie symmetries
Freire, Emilio; Gasull Embid, Armengol; Guillamon Grabolosa, Antoni
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I; Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
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.
Differentiable dynamical systems
Differential equations
Limit cycles
isochrons
Lie symmetries
hyperbolicity
Sistemes dinàmics diferenciables
Equacions diferencials ordinàries
Classificació AMS::34 Ordinary differential equations::34A General theory
Classificació AMS::34 Ordinary differential equations::34C Qualitative theory
Classificació AMS::37 Dynamical systems and ergodic theory::37C Smooth dynamical systems: general theory
Attribution-NonCommercial-NoDerivs 2.5 Spain
http://creativecommons.org/licenses/by-nc-nd/2.5/es/
Article
         

Show full item record

Related documents

Other documents of the same author

Freire, Emilio; Gasull Embid, Armengol; Guillamon Grabolosa, Antoni
Freire, Emilio; Gasull Embid, Armengol; Guillamon Grabolosa, Antoni
Freire, Emilio; Gasull Embid, Armengol; Guillamon Grabolosa, Antoni
Gasull Embid, Armengol; Guillamon Grabolosa, Antoni; Mañosa Fernández, Víctor
Gasull Embid, Armengol; Guillamon Grabolosa, Antoni; Mañosa Fernández, Víctor
 

Coordination

 

Supporters