PIECEWISE LINEAR PERTURBATIONS OF A LINEAR CENTER

Autor(es)

Buzzi, Claudio ^[1] ; Pessoa, Claudio ^[1] ; Torregrosa, Joan ^[2]

Afiliação do(s) autor(es)

^[1] Univ Estadual Paulista, Dept Matemat, BR-15054000 Sao Jose Do Rio Preto - Brazil

^[2] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona - Spain

• Tipo de documento: Artigo Científico
• Fonte: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS; v. 33, n. 9, p. 3915-3936, SEP 2013.
• Citações Web of Science: 36

Resumo

This paper is mainly devoted to the study of the limit cycles that can bifurcate from a linear center using a piecewise linear perturbation in two zones. We consider the case when the two zones are separated by a straight line Sigma and the singular point of the unperturbed system is in Sigma. It is proved that the maximum number of limit cycles that can appear up to a seventh order perturbation is three. Moreover this upper bound is reached. This result confirms that these systems have more limit cycles than it was expected. Finally, center and isochronicity problems are also studied in systems which include a first order perturbation. For the latter systems it is also proved that, when the period function, defined in the period annulus of the center, is not monotone, then it has at most one critical period. Moreover this upper bound is also reached. (AU)

• Processo FAPESP: 11/13152-8 - Teoria qualitativa de campos de vetores polinomiais
• Beneficiário: Cláudio Gomes Pessoa
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 07/06896-5 - Geometria de sistemas de controle, sistemas dinâmicos e estocásticos
• Beneficiário: Luiz Antonio Barrera San Martin
• Modalidade de apoio: Auxílio à Pesquisa - Temático