Planar phase portraits and generic bifurcations of reversible vector fields

• Grant number: 07/04307-2
• Support Opportunities: Scholarships abroad - Research
• Start date: October 07, 2007
• End date: November 23, 2007
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Claudio Aguinaldo Buzzi
• Grantee: Claudio Aguinaldo Buzzi
• Host Investigator: Jaume Llibre
• Host Institution: Instituto de Biociências, Letras e Ciências Exatas (IBILCE). Universidade Estadual Paulista (UNESP). Campus de São José do Rio Preto. São José do Rio Preto , SP, Brazil
• Institution abroad: Universitat Autònoma de Barcelona (UAB), Spain

Abstract

First part: study of the generic bifurcation of codimension one at the class reversible vector field of type (2n+1,n). More precisely, we intend to investigate the occurrence of families of periodic orbits and/or homo/heteroclinic orbits, by using the techniques of Normal Forms and Liapunov-Schmidt reduction. In sequence we will consider perturbation of such systems via KAM Theory and we will study the persistence of such minimal sets. Second part: study of the possible global phase portraits of a system of the form X(x)= L(x) + g(x), where L is its linear part and g is a homogeneous polynomial planar vector field of degree three. Moreover, we will assume that the origin is an elliptical singular point of X and X is reversible of type (2,1). (AU)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

BUZZI, CLAUDIO A.; LLIBRE, JAUME; MEDRADO, JOAO C.; TORREGROSA, JOAN. Bifurcation of limit cycles from a centre in R-4 in resonance 1:N. DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL, v. 24, n. 1, p. 123-137, 2009. (07/04307-2)