The local period function for Hamiltonian systems with applications
Buzzi, Claudio (Universidade Estadual Paulista Julio de Mesquita Filho. Mathematics Department (Brazil))
Carvalho, Yagor Romano (Universidade Estadual Paulista Julio de Mesquita Filho. Mathematics Department (Brazil))
Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2021
Abstract:	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.
Grants:	Ministerio de Economía y Competitividad MTM2016-77278-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617 Ministerio de Ciencia e Innovación PID2019-104658GB-I00
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Period function ; Limit cycles ; Abelian integrals ; Extended complete Chebyshev systems ; Picard-Fuchs differential equations
Published in:	Journal of differential equations, Vol. 280 (April 2021) , p. 590-617, ISSN 1090-2732

DOI: 10.1016/j.jde.2021.01.033

Postprint 23 p, 450.9 KB

The record appears in these collections:
Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
Articles > Published articles