# Connectedness properties of the set where the iterates of an entire function are unbounded

Osborne, John; Rippon, Philip and Stallard, Gwyneth (2017). Connectedness properties of the set where the iterates of an entire function are unbounded. Ergodic Theory and Dynamical Systems, 37(4) pp. 1291–1307.

## Abstract

We investigate the connectedness properties of the set I+(f) of points where the iterates of an entire function f are unbounded. In particular, we show that I+(f) is connected whenever iterates of the minimum modulus of f tend to ∞. For a general transcendental entire function f, we show that I+(f)∪ is always connected and that, if I+(f) is disconnected, then it has uncountably many components, infinitely many of which are unbounded.

## Metrics

### Public Attention

Altmetrics from Altmetric

### Number of Citations

Citations from Dimensions