Abstract of

'Phase Transitions of the Logistic Map with Inhomogeneous Noise'

Noisy alias random dynamical systems in recent years have attracted the interest of physicists and mathematicians, for two basic reasons: Physically, they add a good deal of realism to the theoretical models of many natural phenomena which were hitherto modeled by deterministic dynamical systems, since it has been realized that noise is almost ubiquitous in reality and often significantly affects the behaviour of complicated systems. Mathematically, random dynamical systems present an attractive synthesis of the fields of stochastics and general dynamical systems in which many branches of mathematical physics and pure mathematics converge and generate new insights. In both disciplines, it soon became clear that random dynamical systems possess a number of interesting new properties, most prominently the phenomena noise induced stability, on-off intermittence, and stochastic bifurcations also called noise induced (phase) transitions.