“Generally in the field of complex dynamical systems, my research activities follow mainly two lines: dynamics of entire transcendental maps and quasi-conformal surgery. Related to the first area, I am interested in the complexification of analytic circle dipheomorphisms. I also worked on the parameter space of the exponential family, and on members of this family having Siegel discs. Other works are about Baker domains of general transcendental maps and more recently, Herman rings of meromorphic maps. Related to the second area, I apply quasi-conformal surgery as a mean of obtaining maps between parameter spaces, mainly polynomial parameter spaces.”
His main area of research is dynamical systems, primarily complex analytic dynamics, but also including more general ideas about chaotic dynamical systems. Lately, he has become intrigued with the incredibly rich topological aspects of dynamics, including such things as indecomposable continua, Sierpinski curves, and Cantor bouquets.
I am interested in Teichmuller Theory, Hyperbolic geometry of three manifolds and Complex Dynamical Systems
“I work primarily in complex analysis, Teichmüller theory, and complex dynamics (in one and several variables). ”
“Mes Interets Scientifiques: Systemes dynamiques holomorphes”
“My research interests lie at the interface of geometry and analysis, including classical complex analysis, the geometry of negatively curved spaces, geometric group theory, dynamics of rational maps, and analysis on metric spaces. My current work often relies on an extension of classical results in geometry and analysis to a non-smooth or fractal setting.”
“My research is in the area of complex dynamics and concerns the iteration of transcendental meromorphic functions. I am particularly interested in the possible dimensions of the Julia set and in the structure of the escaping set. I am currently funded by the EPSRC (0.5FT) to work on the project "Baker's conjecture and Eremenko's conjecture: a unified approach" ”
“My research has its origins in complex analysis. I study analytic and meromorphic functions on the complex plane and quasiregular mappings of n-dimensional real space. I am interested in the behaviour under iteration of such functions, and also their value distribution.”
“My research interests include quasiregular dynamics, Teichmüller theory and value distribution theory.”Gallery of quasiregular tangent mapping pictures