The local period function for Hamiltonian systems with applications
| Autor: | Claudio A. Buzzi, Armengol Gasull, Yagor Romano Carvalho |
|---|---|
| Přispěvatelé: | Universidade Estadual Paulista (Unesp), Univ Autonoma Barcelona, Ctr Recerca Matemat |
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Abelian integral
Abelian integrals Dynamical Systems (math.DS) 01 natural sciences Constructive Chebyshev filter Hamiltonian system symbols.namesake Pendulum (mathematics) Taylor series FOS: Mathematics Extended complete Chebyshev systems Applied mathematics Limit (mathematics) 0101 mathematics Mathematics - Dynamical Systems Mathematics Period function Applied Mathematics 010102 general mathematics Function (mathematics) 34C08 34C25 37G15 37J45 010101 applied mathematics Limit cycles Picard-Fuchs differential equations symbols Analysis |
| Zdroj: | Web of Science Repositório Institucional da UNESP Universidade Estadual Paulista (UNESP) instacron:UNESP Dipòsit Digital de Documents de la UAB Universitat Autònoma de Barcelona |
| Popis: | 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. 23 pages |
| Databáze: | OpenAIRE |
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