Published 2023-12-13
Keywords
- Logistic map,
- skew coupling,
- invariant set
How to Cite
Copyright (c) 2023 Revista Integración, temas de matemáticas
This work is licensed under a Creative Commons Attribution 4.0 International License.
Abstract
Our main aim is to study some aspects of the asymptotic evolution of the orbits obtained by iterating the endomorphism $$F_{\mu, \epsilon}(x,y)=( f_\mu(x), f_\mu(y)+\epsilon (x-y)),$$ where $\mu >1$ is the parameter of the logistic family: $ f_\mu(x)=\mu x(1-x)$ and $\epsilon\in (0,1),$ 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 show in detail the construction of a invariant compact in the parameter space, together with a description of the behavior of the preimages of zones in $ \mathbb R^2$ that play an important role in understanding the dynamics of coupling.
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