Triviality of fibers for Misiurewicz parameters in the exponential family

Abstract

We consider the family of holomorphic maps e^z+c and show that fibers of postcritically finite parameters are trivial. This can be seen as the first and simplest class of non-escaping parameters for which we can obtain results about triviality of fibers in the exponential family.

References in corpus (4)

• Iteration of meromorphic functions
• Topological Dynamics of Exponential Maps on their Escaping Sets
• Classification of Escaping Exponential Maps
• A Landing Theorem for Periodic Rays of Exponential Maps

Cited by in corpus (4)

• Escaping endpoints explode
• A landing theorem for entire functions with bounded post-singular sets
• The escaping set in transcendental dynamics
• On postsingularly finite exponential maps