Pau Rabassa (Johann Bernoulli Institute for Mathematics and Computer Science, University of Groningen): Towards a renormalization theory for quasi-periodically forced one dimensional maps

This talk focusses on the study of quasi-periodically forced one
dimensional unimodal maps. These are maps on the cylinder where the
periodic component is a rigid rotation and the other component is a
quasi-periodic perturbation of a map in the interval. For certain
one parametric families of maps in the interval, it is well known
that their bifurcations exhibit a universal behavior, in the sense
that the behavior is the same for a wide class of families. This
universal behavior can be explained as a consequence of the dynamics
of the renormalization operator. We discuss what happens to this
phenomenon when we add a q.p. perturbation to the one dimensional
family of maps. Concretely we show numerical evidences of
self-similarity and universality. We also propose an extension
of the renormalization operator to the q.p. forced case, which
gives a suitable explanation to the previous numerical observations.