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Abstract:
Attractors are invariant compact sets that attract all trajectories of an underlying dynamical system, and hence are crucial to the analysis of dynamical systems. On the one hand, attractors are typically not regular surfaces in the state space but rather more complicated kinds of sets. On the other hand, when the trajectories are complex, the attractor may eventually exhibit strange and chaotic structures. Their interesting and complicated nature motivates extensive studies on attractors in the past decade. The theory of global attractors, that capture the asymptotic behavior of autonomous systems, has been well established over the past decades. More recently a new type of attractors, called pullback attractors, were proposed to investigate asymptotic behavior of non-autonomous and random dynamical systems. The goal of this special session is to present recent developments in the studies of various type of attractors such as global attractors, pull back attractors, random attractors, forward attractors, and strange attractors, etc. The topics include not only general existence and continuity properties of attractors, but also their detailed geometrical structures. A special emphasis will be given to attractors for dynamical systems arising in the applied sciences and engineering.
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