seminar: Flattening, squeezing and the existence of attractors for random dynamical systems
speaker: José Antonio Langa (Universidad de Sevilla)abstract: It is a well known fact that a dissipative dynamical system is usually characterized by a flattening dynamics in the high modes of their trajectories, which leads to the existence of compact global attracting sets. In this talk we show a general theorem on the existence of attractors for random dynamical systems, which also would include the case of non-autonomous differential equations, based on a flattening property on the pullback asymptotic dynamics of the trajectories. We present some applications to stochastic PDEs, which shows the essential non-trivial differences with respect to the deterministic case. On the other hand, we include a discussion on the relationship between flattening and the squeezing property, both in the deterministic and the random cases. We show that the (random) squeezing property is a sufficient condition for a system to be flattening, so that it implies the existence of (random) global attractors.
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