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.

DOI: https://doi.org/10.1017/etds.2015.85

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)∪ \{\infty\} is always connected and that, if I+(f) is disconnected, then it has uncountably many components, infinitely many of which are unbounded.

Viewing alternatives

Download history

Metrics

Public Attention

Altmetrics from Altmetric

Number of Citations

Citations from Dimensions

Item Actions

Export

About

Recommendations