On the Chebyshev property for a new family of functions

We analyze whether a given set of analytic functions is an Extended Chebyshev system. This family of functions appears studying the number of limit cycles bifurcating from some nonlinear vector field in the plane. Our approach is mainly based on the so called Derivation-Division algorithm. We prove...

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Detalhes bibliográficos
Autores: Gasull, Armengol|||0000-0002-1719-8231, Torregrosa, Joan|||0000-0002-2753-1827
Formato: artículo
Fecha de publicación:2012
País:España
Recursos:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:150537
Acesso em linha:https://ddd.uab.cat/record/150537
https://dx.doi.org/urn:doi:10.1016/j.jmaa.2011.09.019
Access Level:acceso abierto
Palavra-chave:Chebyshev system
Number of zeroes of real functions
Derivation-Division algoritm
Limit cycles of planar systems
Descrição
Resumo:We analyze whether a given set of analytic functions is an Extended Chebyshev system. This family of functions appears studying the number of limit cycles bifurcating from some nonlinear vector field in the plane. Our approach is mainly based on the so called Derivation-Division algorithm. We prove that under some natural hypotheses our family is an Extended Chebyshev system and when some of them are not fulfilled then the set of functions is not necessarily an Extended Chebyshev system. One of these examples constitutes an Extended Chebyshev system with high accuracy.