Parameter spaces of families of transcendental functions

Abstract: This lecture is based on joint work with Tao Chen, Nuria Fagella and Yunping Jiang. It is part of a more general program to understand parameter spaces of transcendental maps.

If we perturb a rational function by a topological conjugacy we obtain a rational function, so the dynamics depend on the coefficients, which therefore form a natural parameter space. It is not true that there is a natural way of parameterizing general families of transcendental functions so that a perturbation of the function remains in the family. This makes it difficult to describe how the dynamics varies across these families. We will look at two examples of reasonably general families of transcendental meromorphic functions where one can overcome these difficulties. What this means is that we will be able to describe the properties of the components defined by the bifurcation locus. We will see at the end how these examples fit into the larger program.

complex variablesdynamical systems

Audience: researchers in the topic

CAvid: Complex Analysis video seminar

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