Pure Maths Colloquium: Quasiregular dynamics
17 October 2011 16:00 in CM221
Complex dynamics, the iteration of holomorphic functions in the plane, has been an active area of research for the last 30 years, ever since Douady and Hubbard's work on quadratic polynomials and the Mandelbrot set. In recent years, work has also focussed on the iteration of transcendental entire functions, whose dynamics has significant differences to those of polynomials. A natural generalization of holomorphic functions to the plane and higher dimensions is given by quasiregular mappings. One can iterate quasiregular mappings, and it is an interesting new avenue of research to see to what extent quasiregular dynamics compares to complex dynamics.
In this talk, we will define quasiregular mappings, see why we can consider them natural generalizations of holomorphic functions, and discuss similarities and differences with respect to complex dynamics. As with any self-respecting dynamics talk, there will be pictures.
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