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2022 A characterization of nonautonomous attractors via Stone-Čech compactification
Josiney A. Souza, Pedro F. S. Othechar
Topol. Methods Nonlinear Anal. 59(1): 261-275 (2022). DOI: 10.12775/TMNA.2021.029

Abstract

The present paper deals with the notions of past attractors and repellers for nonautonomous dynamical systems. This uses the topological method of extending functions in order to describe the nonautonomous attractors by means of the prolongational limit sets in the extended phase space. Essentially, for a given nonautonomous dynamical system $(\theta ,\varphi ) $ with base set $P=\mathbb{T}$, where $\mathbb{T}$ is the time $\mathbb{Z}$ or $\mathbb{R}$, and with base flow $\theta $ as the addition, the limit sets $\omega ^{-}( 0) $ and $\omega^{+}( 0) $ in the Stone-Čech compactification $\beta \mathbb{T}$ determine respectively the past and the future of the conduction system.

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Josiney A. Souza. Pedro F. S. Othechar. "A characterization of nonautonomous attractors via Stone-Čech compactification." Topol. Methods Nonlinear Anal. 59 (1) 261 - 275, 2022. https://doi.org/10.12775/TMNA.2021.029

Information

Published: 2022
First available in Project Euclid: 23 March 2022

Digital Object Identifier: 10.12775/TMNA.2021.029

Keywords: Nonautonomous dynamical system , past attractor , Stone-Čech compactification

Rights: Copyright © 2022 Juliusz P. Schauder Centre for Nonlinear Studies

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Vol.59 • No. 1 • 2022
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