A Chebyshev criterion with applications

We show that a family of certain definite integrals forms a Chebyshev system if two families of associated functions appearing in their integrands are Chebyshev systems as well. We apply this criterion to several examples which appear in the context of perturbations of periodic non-autonomous ODEs t...

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Detalhes bibliográficos
Autores: Gasull, Armengol|||0000-0002-1719-8231, Geyer, Anna|||0000-0003-1834-2108, Mañosas, Francesc|||0000-0003-2535-0501
Formato: artículo
Fecha de publicación:2020
País:España
Recursos:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:228117
Acesso em linha:https://ddd.uab.cat/record/228117
https://dx.doi.org/urn:doi:10.1016/j.jde.2020.05.015
Access Level:acceso abierto
Palavra-chave:Chebyshev system
Bifurcation of limit cycles
Abelian integral
Melnikov function
Descrição
Resumo:We show that a family of certain definite integrals forms a Chebyshev system if two families of associated functions appearing in their integrands are Chebyshev systems as well. We apply this criterion to several examples which appear in the context of perturbations of periodic non-autonomous ODEs to determine bounds on the number of isolated periodic solutions, as well as to persistence problems of periodic solutions for perturbed Hamiltonian systems.