Random attractors -- general properties, existence and applications to stochastic bifurcation theory (Q1576765)

This paper deals with a stochastic version of attractors. The author introduces the new concept of random attractors and studies a nontrivial example: The random Duffing-van der Pol oscillator. Moreover the author shows that by the same example, random attractors provide an important tool to analyze the bifurcation behaviour of stochastically perturbed dynamical systems. In particular, he introduces new methods and techniques in order to study the Hopf bifurcation scenario of the random Duffing-van der Pol equation in detail. The relationship of random attractors to invariant measures and unstable sets is investigated.