A characterization of nonautonomous attractors via Stone-Čech compactification - Souza, Josiney A.; Othechar, Pedro F. S. (Topological Methods in Nonlinear Analysis, 2022)
The present paper deals with the notions of past attractors andrepellers for nonautonomous dynamical systems. This uses the topologicalmethod of extending functions in order to describe the nonautonomousattractors by means of the prolongational limit sets in the extended phasespace. Essentially, for a given nonautonomous dynamical system$(θ ,φ ) $ with base set $P=\mathbb{T}$, where $\mathbb{T}$is the time $\mathbb{Z}$ or $\mathbb{R}$, and with base flow $θ $ asthe addition, the limit sets $ω ^{-}( 0) $ and$ω^{+}( 0) $ in the Stone-Čech compactification$β \mathbb{T}$ determine respectively the past and the future of the conduction system.