Escaping Points of Exponential Maps

By Dierk Schleicher, Johannes Zimmer. 2003

135 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/6dd3555b74d9c54934d574d682d37c2d4c187d3e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

The dynamical fine structure of iterated cosine maps and a dimension paradox (2004, background): “In [K], Karpi´nska had shown that for exponential maps z 7→ λexp(z) with attracting fixed points (in particular, 0 SZ1 ] to arbitrary exponential maps: not all rays land, and not all rays which land have escaping landing points, but the union of all rays still has dimension 1, while the set of esca”
Dynamic rays of bounded-type entire functions (2007, background): “ich class that one can explicitly write down.) It seems that it was partly these developments that led Eremenko to pose the above-mentioned questions in his 1989 paper. More recently, it was shown in [SZ] that every escaping point of every exponential map can be connected to ∞ by a curve consisting ”
Periodic Points and Dynamic Rays of Exponential Maps (2003, methodology): “In this section, we brie∞y recollect some facts from [ SZ2 ].”
Slow escaping points of meromorphic functions (2008, background): “These open curves are in Z(f), and even in A(f); see [34] and [25].”
Topological dynamics of exponential maps on their escaping sets (2003, background): “While exponential maps are generally not conjugate on their sets of escaping points, the situation is quite different for parameters with an attracting (or parabolic) periodic orbit, since such maps are expanding on their Julia sets.”
Hausdorff dimension and conformal measures of Feigenbaum Julia sets (2004, background): “For other interesting properties of the measure and dimension of transcendental Julia sets, see [L2, R, K, SZ , UZ].”
On questions of Fatou and Eremenko (2004, background): “It is known that this property does hold for certain families of functions (see [6] and [12]), but it is still not known whether this property holds in general.”