S. Yu. Pilyugin

Attractors of Reaction Diffusion Systems on Infinite Lattices

AbstractIn this paper, we study global attractors for implicit discretizations of a semilinear parabolic system on the line. It is shown that under usual dissipativity conditions there exists a global (Zu,Zρ)-attractor

Theory of pseudo-orbit shadowing in dynamical systems

A

Periodic shadowing and Ω-stability

in the sense of Babin-Vishik and Mielke-Schneider. Here Zρ is a weighted Sobolev space of infinite sequences with a weight that decays at infinity, while the space Zu carries a locally uniform norm obtained by taking the supremum over all Zρ norms of translates. We show that the absorbing set containing

Continuous dependence of attractors on the shape of domain

A

Analogues of Takens’ theorems for generalized actions of the group ℤ∞

can be taken uniformly bounded (in the norm of Zu) for small time and space steps of the discretization. We establish the following upper semicontinuity property of the attractor