Topological Dynamics of Exponential Maps on their Escaping Sets

Details Topological Dynamics of Exponential Maps on their Escaping Sets Topological Dynamics of Exponential Maps on their Escaping Sets

2003-09-05

arxiv.org/abs/math/0309107v3

Ergodic Theory and Dynam. Systems 26 (2006), No. 6, 1939-1975

Mathematics

Dynamical Systems

38 pages, 3 figures. // V3: Several typos fixed; some overall revision; parts of the material in Sections 5, 7 and 11 have bee

Scientific paper

10.1017/S0143385706000435

We develop an abstract model for the dynamics of an exponential map $z\mapsto \exp(z)+\kappa$ on its set of escaping points and, as an analog of Boettcher's theorem for polynomials, show that every exponential map is conjugate, on a suitable subset of its set of escaping points, to a restriction of this model dynamics. Furthermore, we show that any two attracting and parabolic exponential maps are conjugate on their sets of escaping points; in fact, we construct an analog of Douady's "pinched disk model" for the Julia sets of these maps. On the other hand, we show that two exponential maps are generally not conjugate on their sets of escaping sets. Using the correspondence with our model, we also answer several questions about escaping endpoints of external rays, such as when a ray is differentiable in such an endpoints or how slowly these endpoints can escape to infinity.

Affiliated with

Also associated with

No associations

Rating

Topological Dynamics of Exponential Maps on their Escaping Sets 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 Topological Dynamics of Exponential Maps on their Escaping Sets, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Topological Dynamics of Exponential Maps on their Escaping Sets will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-358149