Complex Dynamical Systems

Mark Elin, Marina Levenshtein, David Shoikhet, Fiana Yacobzon, Filippo Bracci (Universitá di Roma “Tor Vergata”, Italy), Manuel D. Contreras (Universidad de Sevilla), Santiago Díaz-Madrigal (Universidad de Sevilla) and Simeon Reich (Technion)
The development of complex dynamical systems has been the subject of research from the beginning of the 20th century. One of the first applicable models for complex dynamical systems arose from studies of stochastic branching processes in the growth of families and populations. Interest in these models has further increased because of their connections to chemical and nuclear chain reactions, the theory of cosmic radiation, and many other biological and physical problems.
The examination of these problems is based on one-parameter semigroups of holomorphic self-mappings of the unit disk of a complex plane, which is our sphere of interest. We study the asymptotic behavior of discrete and continuous time semigroups (in one-dimensional and multi-dimensional settings), rates of convergence of semigroups to their attractive fixed points, and boundary rigidity problems for semigroups and their generators. We are also interested in criteria of analytic extension of semigroups in their parameter.