Doubly periodic Julia and Fatou sets for iterated meromorphic functions: dynamics on unbounded components

Abstract: Elliptic functions give rise under iteration to Julia and Fatou sets that are invariant under the action of translation by elements of the period lattice. However doubly periodic Julia and Fatou sets can arise for non-elliptic meromorphic functions as well. Unbounded Fatou components in both settings exhibit dynamics different from those of rational maps and are called toral bands since they can be viewed on a torus (a fundamental region in the plane with identifications). We discuss how the dynamics depend on the function and the lattice, both its shape and its size, and what parameter choices produce unbounded components. We will also touch on the stability and connectivity of these components.

complex variablesdynamical systems

Audience: researchers in the topic

CAvid: Complex Analysis video seminar

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