On the set where the iterates of an entire function are bounded

Abstract

We show that for a transcendental entire function the set of points whose orbit under iteration is bounded can have arbitrarily small positive Hausdorff dimension.

7 pages

References in corpus (1)

• Fast escaping points of entire functions

Cited by in corpus (6)

• Connectedness properties of the set where the iterates of an entire function are bounded
• Foundations for an iteration theory of entire quasiregular maps
• The bungee set in quasiregular dynamics
• Dynamical sets whose union with infinity is connected
• On the dimension of the boundaries of attracting basins of entire maps
• On slow escaping and non-escaping points of quasimeromorphic mappings