Combinatorics of Bifurcations in Exponential Parameter Space

Details Combinatorics of Bifurcations in Exponential Parameter Space Combinatorics of Bifurcations in Exponential Parameter Space

2004-08-02

arxiv.org/abs/math/0408011v2

In: Transcendental dynamics and complex analysis. In honour of Noel Baker (Rippon and Stallard, eds); London Mathematical Soci

Mathematics

Dynamical Systems

48 pages, 5 figures. V2: The article (particularly Section 6 and 7) was revised to improve the exposition; some figures were a

Scientific paper

We give a complete combinatorial description of the bifurcation structure in the space of exponential maps $z\mapsto\exp(z)+\kappa$. This combinatorial structure is the basis for a number of important results about exponential parameter space. These include the fact that every hyperbolic component has connected boundary, a classification of escaping parameters, and the fact that all dynamic and parameter rays at periodic addresses land.

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