A note on the topology of escaping endpoints

Abstract

We study topological properties of the escaping endpoints and fast escaping endpoints of the Julia set of complex exponential $\exp (z)+a$ when $a\in (-\infty ,-1)$. We show neither space is homeomorphic to the whole set of endpoints. This follows from a general result stating that for every transcendental entire function $f$, the escaping Julia set $I(f)\cap J(f)$ is first category.

4 pages

References in corpus (1)

• On cohesive almost zero-dimensional spaces

Cited by in corpus (1)

• Exponential iteration and Borel sets