Gastvortrag von Herrn Peter Kloeden, zum Thema: Forward attractors and limit sets of nonautonomous difference equations
VeranstaltungsortN.2.01Veranstalter Institut für MathematikBeschreibungThe theory of nonautonomous dynamical systems has undergone majordevelopment during the past 19 years since I talked about attractors ofnonautonomous difference equations at ICDEA Poznan in 1998.Two types of attractors consisting of invariant families of sets have beendesigned for nonautonomous difference equations, one using pullback convergencewith information about the system in the past and the other usingforward convergence with information about the system in the future. Inboth cases, the component sets are constructed using a pullback argumentwithin a positively invariant family of sets. The forward attractor so constructedalso uses information about the past, which is very restrictive andnot essential for determining future behaviour. The forward asymptotic behaviourcan also be described through the omega-limit set of the system.Thisset is closely related to what Vishik called the uniform attractor although itneed not be invariant. It is shown to be asymptotically positively invariantand also, provided a future uniformity condition holds, also asymptoticallypositively invariant. Hence this omega-limit set provides useful informationabout the behaviour in current time during the approach to the future limit.Vortragende(r)Peter KloedenKontaktsenka haznadar (senka.haznadar@aau.at)
