Connected escaping sets of exponential maps

Abstract

We show that for many complex parameters a, the set of points that converge to infinity under iteration of the exponential map f(z)=e^z+a is connected. This includes all parameters for which the singular value escapes to infinity under iteration.

9 pages; minor revisions from Version 1

References in corpus (2)

• Semiconjugacies, pinched Cantor bouquets and hyperbolic orbifolds
• On the connectivity of the escaping set for complex exponential Misiurewicz parameters

Cited by in corpus (9)

• Fast escaping points of entire functions
• Escaping endpoints explode
• Connectedness properties of the set where the iterates of an entire function are bounded
• Connectedness properties of the set where the iterates of an entire function are unbounded
• The escaping set in transcendental dynamics
• Spiders' webs in the Eremenko-Lyubich class
• Dynamics of meromorphic functions outside a countable set of essential singularities
• The iterated minimum modulus and conjectures of Baker and Eremenko
• On escaping sets of some families of entire functions and dynamics of composite entire functions