Bifurcation and Hausdorff dimension in families of chaotically driven maps with multiplicative forcing

We consider the bifurcation of invariant graphs in a parametrized skew-product system with hyperbolic base-map. In contrast to quasi-periodically driving systems, the hyperbolic driving causes a smooth bifurcation process from a point of view of the dimension theory.

We mainly discuss this phenomenon using the thermodynamic formalisms. (Joint work with Gerhard Keller)