Rigidity of escaping dynamics for transcendental entire functions

Details Rigidity of escaping dynamics for transcendental entire functions Rigidity of escaping dynamics for transcendental entire functions

2006-05-02

arxiv.org/abs/math/0605058v3

Acta Mathematica 203 (2009), no 2, 235 --267

Mathematics

Dynamical Systems

28 pages; 2 figures. Final version (October 2008). Various modificiations were made, including the introduction of Proposition

Scientific paper

10.1007/s11511-009-0042-y

We prove an analog of Boettcher's theorem for transcendental entire functions in the Eremenko-Lyubich class B. More precisely, let f and g be entire functions with bounded sets of singular values and suppose that f and g belong to the same parameter space (i.e., are *quasiconformally equivalent* in the sense of Eremenko and Lyubich). Then f and g are conjugate when restricted to the set of points which remain in some sufficiently small neighborhood of infinity under iteration. Furthermore, this conjugacy extends to a quasiconformal self-map of the plane. We also prove that this conjugacy is essentially unique. In particular, we show that an Eremenko-Lyubich class function f has no invariant line fields on its escaping set. Finally, we show that any two hyperbolic Eremenko-Lyubich class functions f and g which belong to the same parameter space are conjugate on their sets of escaping points.

Affiliated with

Also associated with

No associations

Rating

Rigidity of escaping dynamics for transcendental entire functions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Rigidity of escaping dynamics for transcendental entire functions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Rigidity of escaping dynamics for transcendental entire functions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-184451