Classification of Escaping Exponential Maps

Abstract

We give a complete classification of the set of parameters $\kappa$ for which the singular value of $E_{\kappa }:z\mapsto \exp (z)+\kappa$ escapes to infinity under iteration. In particular, we show that every path-connected component of this set is a curve to infinity.

13 pages, 1 figure -- final version (to appear in Proc. AMS); only minor changes from v5

References in corpus (4)

• Topological Dynamics of Exponential Maps on their Escaping Sets
• A Landing Theorem for Periodic Rays of Exponential Maps
• On Nonlanding Dynamic Rays of Exponential Maps
• Parameter rays for the exponential family

Cited by in corpus (15)

• A Landing Theorem for Periodic Rays of Exponential Maps
• Escaping endpoints explode
• Connected escaping sets of exponential maps
• Bifurcations in the Space of Exponential Maps
• Geometrically finite transcendental entire functions
• The escaping set of the exponential
• Hyperbolic Components in Exponential Parameter Space
• Non-escaping endpoints do not explode
• Triviality of fibers for Misiurewicz parameters in the exponential family
• Infinite-dimensional Thurston theory and transcendental dynamics I: infinite-legged spiders
• The escaping set in transcendental dynamics
• Infinite-dimensional Thurston theory and transcendental dynamics II: classification of entire functions with escaping singular orbits
• Ergodic exponential maps with escaping singular behaviours
• Infinite-dimensional Thurston theory and transcendental dynamics III: entire functions with escaping singular orbits in the degenerate case
• Infinite-dimensional Thurston theory and transcendental dynamics IV: dependence on parameters and escape on (pre-)periodic rays