The Relationships Between Discrete Dynamical Systems in Topological Spaces and their respective Hyperextensions to sets of Compact Spaces

Keywords: Function, hyperextension, dynamic system, individual chaos, collective chaos

Abstract

Several studies have been carried out related to the analysis of the relationship with respect to the dynamic properties of f and its hyperextension ̄f. However, the literature regarding the analysis of the effects of individual and collective chaos on their behaviour is scarce. Therefore, in this article several conjectures and questions are established according to the affectation of individual chaos in an ecosystem and its chaotic behaviour within the dynamics of this ecosystem, but as a whole. Thus, in the first instance, an introduction to the conceptualization of topological transitivity, chaos in the Devaney sense and how they are specified in continuous linear operators arranged in a Fréchet space (hypercyclic operators) will be established. In addition, the different notions of chaos that can occur depending on the relationship of the function, and its hyperextension will be described, to finally corroborate the present chaos with greater force than Devaney’s according to the strong periodic specification property, the same one that applies to both f and a ̄f with the purpose of verifying the  directionality in which individual and collective chaos can occur.

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Author Biographies

Héctor Méndez-Gómez, Universidad de Costa Rica, sede regional del Pacífico – Costa Rica.

Matemático, Universidad de Costa Rica, Máster Universitario Investigación Matemática, Universitat Politècnica de Vàlencia, España. Docente en matemática de la Universidad de Costa Rica, sede regional del Pacífico – Costa Rica.

Jorge Luís Yaulema-Castañeda, Escuela Superior Politécnica del Chimborazo, Ecuador.

Ingeniero Electrónico, Universidad Politécnica Salesiana, Máster Universitario en Investigación Matemática – Universidad de Valencia. Docente en la Escuela Superior Politécnica del Chimborazo – Ecuador.

Paulina Fernanda Bolaños-Logroño, Escuela Superior Politécnica del Chimborazo, Ecuador.

Ingeniera Electrónica, Escuela Superior Politécnica del Chimborazo, Magister en Sistemas de Control y Automatización Industrial - Escuela Superior Politécnica del Chimborazo – Ecuador, Máster Universitario en Estadística Aplicada – Universidad de Granada - España. Docente en la Escuela Superior Politécnica del Chimborazo – Ecuador.

Fernando Ricardo Márquez-Sañay , Escuela Superior Politécnica del Chimborazo, Ecuador.

Ingeniero Mecánico, Escuela Superior Politécnica de Chimborazo, Máster Universitario en Matemáticas y Computación – Universidad Internacional de la Rioja - España. Docente en la Escuela Superior Politécnica del Chimborazo – Ecuador.

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Published
2023-05-02
How to Cite
Méndez-Gómez, H., Yaulema-Castañeda, J. L., Bolaños-Logroño, P. F., & Márquez-Sañay , F. R. (2023). The Relationships Between Discrete Dynamical Systems in Topological Spaces and their respective Hyperextensions to sets of Compact Spaces. Journal of the University of Zulia , 14(40), 43-83. https://doi.org/10.46925//rdluz.40.04