Complex dynamics studies the evolution of a complex manifold under the action of a holomorphic map. In this proposal we study the dynamical systems generated by transcendental (either entire or meromorphic) maps acting on the complex plane. By using a wide range of classic and new techniques, we investigates epecially the combinatorics of these maps: that is to say, we build relations between the dynamics of the transcendental map on some specific subset of the complex plane and the dynamics of the shift map on the space of infinite sequences over the integers. Combinatorics in this setting is a powerful tool to understand the dynamics of transcendental maps and to understand the structure of specific families of transcendental maps. The study of combinatorics for transcendental maps is also likely to offer new insights in the combinatorics for rational maps and possibly in other areas of complex dynamical systems, like the systems generated by the iteration of holomorphic maps on manifolds with more than one complex dimension.
Field of science
- /natural sciences/mathematics/pure mathematics
- /natural sciences/mathematics/applied mathematics/dynamical systems
Call for proposal
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