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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

The local period function for Hamiltonian systems with applications

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Buzzi, Claudio A. [1] ; Carvalho, Yagor Romano [1] ; Gasull, Armengol [2, 3]
Total Authors: 3
[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
Total Affiliations: 3
Document type: Journal article
Source: Journal of Differential Equations; v. 280, p. 590-617, APR 15 2021.
Web of Science Citations: 1

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)

FAPESP's process: 19/10269-3 - Ergodic and qualitative theories of dynamical systems II
Grantee:Claudio Aguinaldo Buzzi
Support Opportunities: Research Projects - Thematic Grants
FAPESP's process: 16/00242-2 - Bifurcation of piecewise smooth systems with singular borders via regularization
Grantee:Yagor Romano Carvalho
Support Opportunities: Scholarships in Brazil - Doctorate
FAPESP's process: 18/05098-2 - Study of limit cycles in piecewise smooth systems on the cylinder
Grantee:Yagor Romano Carvalho
Support Opportunities: Scholarships abroad - Research Internship - Doctorate