## Institute for Mathematical Sciences

## Preprint ims12-06

** Anna Miriam Benini, Mikhail Lyubich**
*Repelling periodic points and landing of rays for post-singularly bounded exponential maps *

Abstract: We show that repelling periodic points are landing points of periodic rays for exponential maps whose singular value has bounded orbit.
For polynomials with connected Julia sets, this is a celebrated theorem by
Douady, for which we present a new proof. In both cases we also show that
points in hyperbolic sets are accessible by at least one and at most
finitely many rays. For exponentials this allows us to conclude that the
singular value itself is accessible.

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