On the existence of infinite heteroclinic cycles in polynomial systems and its dynamic consequences


Autoria(s): Messias, Marcelo; Meneguette, M.; Simos, T. E.; Tsitouras, C.
Contribuinte(s)

Universidade Estadual Paulista (UNESP)

Data(s)

20/05/2014

20/05/2014

01/01/2004

Resumo

In this work we consider the dynamic consequences of the existence of infinite heteroclinic cycle in planar polynomial vector fields, which is a trajectory connecting two saddle points at infinity. It is stated that, although the saddles which form the cycle belong to infinity, for certain types of nonautonomous perturbations the perturbed system may present a complex dynamic behavior of the solutions in a finite part of the phase plane, due to the existence of tangencies and transversal intersections of their stable and unstable manifolds. This phenomenon might be called the chaos arising from infinity. The global study at infinity is made via the Poincare Compactification and the argument used to prove the statement is the Birkhoff-Smale Theorem. (c) 2004 WILEY-NCH Verlag GmbH & Co. KGaA, Weinheim.

Formato

261-264

Identificador

Icnaam 2004: International Conference on Numerical Analysis and Applied Mathematics 2004. Weinheim: Wiley-v C H Verlag Gmbh, p. 261-264, 2004.

http://hdl.handle.net/11449/39610

WOS:000227717500068

Idioma(s)

eng

Publicador

Wiley-Blackwell

Relação

Icnaam 2004: International Conference on Numerical Analysis and Applied Mathematics 2004

Direitos

closedAccess

Tipo

info:eu-repo/semantics/conferencePaper