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Gastvortrag von Herrn Peter Kloeden, zum Thema: Forward attractors and limit sets of nonautonomous difference equations

15. Mai 2019 um 11:00

Veranstaltungskategorie Vortrag |Foto: kasto/


Institut für Mathematik


The theory of nonautonomous dynamical systems has undergone major
development during the past 19 years since I talked about attractors of
nonautonomous difference equations at ICDEA Poznan in 1998.
Two types of attractors consisting of invariant families of sets have been
designed for nonautonomous difference equations, one using pullback convergence
with information about the system in the past and the other using
forward convergence with information about the system in the future. In
both cases, the component sets are constructed using a pullback argument
within a positively invariant family of sets. The forward attractor so constructed
also uses information about the past, which is very restrictive and
not essential for determining future behaviour. The forward asymptotic behaviour
can also be described through the omega-limit set of the system.This
set is closely related to what Vishik called the uniform attractor although it
need not be invariant. It is shown to be asymptotically positively invariant
and also, provided a future uniformity condition holds, also asymptotically
positively invariant. Hence this omega-limit set provides useful information
about the behaviour in current time during the approach to the future limit.

Peter Kloeden

senka haznadar (senka [dot] haznadar [at] aau [dot] at)


15. Mai 2019 um 11:00 Uhr
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