Fast escaping points of entire functions

By P. Rippon, G. Stallard. 2010

122 citations recorded by the source corpus.

Let f be a transcendental entire function and let A(f) denote the set of points that escape to infinity ‘as fast as possible’ under iteration. By writing A(f) as a countable union of closed sets, called ‘levels’ of A(f), we obtain a new understanding of the structure of this set. For example, we show that if U is a Fatou component in A(f), then ∂U⊂A(f) and this leads to significant new results and considerable improvements to existing results about A(f). In particular, we study functions for which A(f), and each of its levels, has the structure of an ‘infinite spider's web’. We show that there are many such functions and that they have a number of strong dynamical properties. This new structure provides an unexpected connection between a conjecture of Baker concerning the components of the Fatou set and a conjecture of Eremenko concerning the components of the escaping set.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9dc5f33235ea54a51a7d03fff95d3b0c40c33ded

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In Applied Mathematics

1. Walter Bergweiler
2. G. Stallard
3. P. Rippon
4. Lasse Rempe

In Geometry and Topology

1. Walter Bergweiler
2. G. Stallard
3. P. Rippon
4. Lasse Rempe

In Mathematical Physics

1. Walter Bergweiler
2. G. Stallard
3. P. Rippon
4. Lasse Rempe

Citations in the corpus

• Multiply connected wandering domains of entire functions (2011, methodology): “We remark that [22] gives a special case of this result but Eremenko’s technique allows for the flexibility described below; see [44] for more details and also [15] for a version of Wiman–Valiron theory that allows this technique to be applied to meromorphic functions with a direct tract.”