Parameter spaces in complex dynamics and related topics

Quasiconformal equivalence of transcendental functions

speaker: James Waterman (Stony Brook Universit)

abstract: By Böttcher’s theorem, two polynomials of the same degree are conformally conjugate in a neighbourhood of infinity. An analogue of this result holds for transcendental entire functions in the Eremenko-Lyubich class B, by results of Rempe. In particular, if two entire functions map near infinity in the same way up to quasiconformal change of coordinates, then they are quasiconformally conjugate on the set of points that remain sufficiently large. This suggests that these eventual quasiconformal equivalence classes play the role of the degree of a polynomial. We discuss how to describe these classes. Joint work in progress with Lasse Rempe.

timetable:
Mon 27 May, 16:45 - 17:25, Aula Dini
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