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...
| Autores: | , , |
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| 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 |
| 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. |
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