Abstract

OSUNA, Osvaldo  and  ROJAS-MILLA, Cristian Jesús. Dynamical aspects of skew coupling of the logistic family. Integración - UIS [online]. 2023, vol.41, n.2, pp.125-146.  Epub Aug 09, 2023. ISSN 0120-419X.  https://doi.org/10.18273/revint.v41n2-2023004.

Our main aim is to study some aspects of the asymptotic evolution of the orbits obtained by iterating the endomorphism F µ,c (x, y) = (f µ (x), f µ (y) + c(x − y)), where > 1 is the parameter of the logistic family: f (x) = x(1 x) and $\epsilon ϵ$ (0;1); is the coupling parameter. This biparametric map is hybrid between two classics in the theory of dynamical systems, the paradigmatic quadratic map and the skew coupling. The main result will be to construct in detail for certain parameters (μ, $ϵ$) an invariant compact set. As well as a study of the asymptotic behavior within this compact and its complement, for this we obtain a description of the behavior of the preimages of zones in ℝ2 that play an important role in understanding the dynamics of the coupling.

Keywords : Logistic map; skew coupling; invariant compact set.

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