Complex Dynamics

Complex Stamp

Our general goal is to describe  the dynamical and parameter plane given by the iteration of holomorphic maps of the complex plane or the Riemann sphere. In  particular, we focus our attention to transcendental entire  or meromorphic families (standard map, complex exponential family,  Newton method applied to entire maps, etc) or rational iteration.

In any of those settings our aproach is mostly topological including the description of the the Julia set, the study of the boundary of Siegel discs,  the distribution of Herman rings, the classificaion of the Baker domains, the properties of the bifurcation locus, etc.

The main tools we use are the quasiconformal surgery, symbolic dynamics and complex analysis.

Some international researches who we work together with are Krzysztof Baranski, Xavier Buff, Bodil Branner, Bob Devaney, Lucas Geyer and Mónica Moreno-Rocha, among others.