Invariant parallels, invariant meridians and limit cycles of polynomial vector fields on some 2-dimensional algebraic tori in R^3
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Rebollo-Perdomo, Salomón (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2013
Abstract:	We consider the polynomial vector fields of arbitrary degree in R3 having the 2-dimensional algebraic torus T2(l, m, n) = {(x, y, z) ∈ R3: (x2l + y2m − r2)2 + z2n − 1 = 0}, where l, m and n positive integers, and r ∈ (1, ∞), invariant by their flow. We study the possible configurations of invariant meridians and parallels that these vector fields can exhibit on T2(l, m, n). Furthermore we analyze when these invariant meridians or parallels are limit cycles.
Grants:	Ministerio de Ciencia y Tecnología MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Polynomial vector fields ; Invariant parallel ; Invariant meridian ; Limit cycles ; Periodic orbits ; 2-dimensional torus
Published in:	Journal of dynamics and differential equations, Vol. 25 Núm. 3 (2013) , p. 777-793, ISSN 1572-9222

DOI: 10.1007/s10884-013-9315-4

Postprint 16 p, 384.2 KB

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