Random dynamical systems with bounded noise: a boundary mapping approachMI 03.06.011 (Boltzmannstr. 3, 85748 Garching)

We consider discrete-time random dynamical systems with uniform spherical noise and introduce a geometric approach to study the compound behaviour of such systems. The key insight of this novel approach is that the boundary of attractors can be represented as invariant sets of a deterministic finite-dimensional mapping, the so-called boundary mapping, that acts on the unit tangent bundle of the phase space. We address questions regarding the persistence of attractors and the nature of bifurcations in this context.