The local period function for Hamiltonian systems with applications

Autor(es)

Buzzi, Claudio A. ^[1] ; Carvalho, Yagor Romano ^[1] ; Gasull, Armengol ^{[2, 3]}

Afiliação do(s) autor(es)

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

^[2] Univ Autonoma Barcelona, Dept Matemat, Edif Cc, Cerdanyola Del Valles 08193, Barcelona - Spain

^[3] Ctr Recerca Matemat, Edif Cc, Campus Bellaterra, Cerdanyola Del Valles 08193, Barcelona - Spain

• Tipo de documento: Artigo Científico
• Fonte: Journal of Differential Equations; v. 280, p. 590-617, APR 15 2021.
• Citações Web of Science: 1

Resumo

In the first part of the paper we develop a constructive procedure to obtain the Taylor expansion, in terms of the energy, of the period function for a non-degenerated center of any planar analytic Hamiltonian system. We apply it to several examples, including the whirling pendulum and a cubic Hamiltonian system. The knowledge of this Taylor expansion of the period function for this system is one of the key points to study the number of zeroes of an Abelian integral that controls the number of limit cycles bifurcating from the periodic orbits of a planar Hamiltonian system that is inspired by a physical model on capillarity. Several other classical tools, like for instance Chebyshev systems are applied to study this number of zeroes. The approach introduced can also be applied in other situations. (C) 2021 Elsevier Inc. All rights reserved. (AU)

• Processo FAPESP: 19/10269-3 - Teorias ergódica e qualitativa dos sistemas dinâmicos II
• Beneficiário: Claudio Aguinaldo Buzzi
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 16/00242-2 - Bifurcações de Sistemas Suaves por Partes com Bordos Singulares via Regularização
• Beneficiário: Yagor Romano Carvalho
• Modalidade de apoio: Bolsas no Brasil - Doutorado
• Processo FAPESP: 18/05098-2 - Estudo de ciclos limite em sistemas suaves por partes no cilindro
• Beneficiário: Yagor Romano Carvalho
• Modalidade de apoio: Bolsas no Exterior - Estágio de Pesquisa - Doutorado