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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Bibliographic Details
Authors: Gasull, A., Valls, C.
Format: article
Status:Versión aceptada para publicación
Publication Date:2021
Country:España
Institution:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repository:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:2072/535429
Online Access:http://hdl.handle.net/2072/535429
Access Level:Open access
Keyword:bifurcation
difference equations
Discrete non-autonomous dynamical systems
Melnikov functions
periodic sequences
Description
Summary: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. © 2021 Informa UK Limited, trading as Taylor & Francis Group.