Discrete Melnikov functions

We consider non-autonomous N-periodic discrete dynamical systems of the form (Formula presented.) having when (Formula presented.) an open continuum of initial conditions such that the corresponding sequences are N-periodic. From the study of some variational equations of low order, we obtain succes...

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Detalles Bibliográficos
Autores: Gasull, Armengol|||0000-0002-1719-8231, Valls, Clàudia|||0000-0001-8279-1229
Tipo de recurso: artículo
Fecha de publicación:2022
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:257089
Acceso en línea:https://ddd.uab.cat/record/257089
https://dx.doi.org/urn:doi:10.1080/10236198.2021.1970147
Access Level:acceso abierto
Palabra clave:Discrete non-autonomous dynamical systems
Periodic sequences
Melnikov functions
Difference equations
Bifurcation
Descripción
Sumario:We consider non-autonomous N-periodic discrete dynamical systems of the form (Formula presented.) having when (Formula presented.) an open continuum of initial conditions such that the corresponding sequences are N-periodic. From the study of some variational equations of low order, we obtain successive maps, that we call discrete Melnikov functions, such that the simple zeroes of the first one that is not identically zero control the initial conditions that persist as N-periodic sequences of the perturbed discrete dynamical system. We apply these results to several examples, including some Abel-type discrete dynamical systems and some non-autonomous perturbed globally periodic difference equations.