Mathematical Sciences: Complex Analytic Dynamics

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Bob Devaney will continue his exciting work on planar dynamical systems. This is part of a program to extend the understanding of rational maps to more general maps in the complex plane. He will continue to study the Julia sets of selected one-parameter families of mappings. These form theboundaries between points with unbounded iterates and those which remain in some fixed region. His innovative use of movies in these studies has been very instructive in our understanding of the dynamics of entire functions, and now seems likely to bear fruit in his investigations of non-analytic dynamics. Devaney will also turn his attention to the bifurcation diagrams of these families. In the realm of analytic dynamics Devaney will work to understand the local dynamics of entire maps near an essential singularity. This is important since one of the distinguishing features of entire functions is the presence of an essential singularity at infinity. In order to extend earlier work to the non-analytic setting he will study non-rational meromorphic functions. There appear to be new dynamical phenomena displayed by the Julia sets of these functions. A final topic for investigation will be the bifurcation structure of the area preserving Henon maps.