On questions of Fatou and Eremenko
By P. Rippon, G. Stallard. 2004
101 citations recorded by the source corpus.
Let $f$ be a transcendental entire function and let $I(f)$ be the set of points whose iterates under $f$ tend to infinity. We show that $I(f)$ has at least one unbounded component. In the case that $f$ has a Baker wandering domain, we show that $I(f)$ is a connected unbounded set.
Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/5890b29456ea9aab1f2ca42c75a77c52ca3ec171
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
- Lasse Rempe
- Walter Bergweiler
- G. Stallard
- P. Rippon
- Dierk Schleicher
- Günter Rottenfusser
- Johannes Ruckert
- Christopher J. Bishop
In Geometry and Topology
In Mathematical Physics
- Lasse Rempe
- Walter Bergweiler
- G. Stallard
- P. Rippon
- Dierk Schleicher
- Günter Rottenfusser
- Johannes Ruckert
- Christopher J. Bishop
Citations in the corpus
- On a question of Eremenko concerning escaping components of entire functions (2006, methodology): “Rippon and Stallard [8] prove that, for any transcendental entire function f , the set A(f) ⊂ I(f) introduced by Bergweiler and Hinkkanen [1] has only unbounded components (and this set does, in fact, satisfy the analog of (c)).”
- Multiply connected wandering domains of entire functions (2011, background): “Some further results are known about multiply connected wandering domains; for example [41], they are contained in the fast escaping set A(f).”
- Iteration of entire functions (2014, background): “4 can be found there, as well as in [33].”
- Slow escaping points of meromorphic functions (2008, background): “The set A(f) has many properties that make it easier to work with than I(f); for example, all its components are unbounded [29], whereas for I(f) this is an open question asked by Eremenko in [15].”
- Dynamic rays of bounded-type entire functions (2007, background): “many times. In the next section, we introduce a property, called a head-start condition, which is designed precisely so that this does not occur. As mentioned in the introduction, Rippon and Stallard [RiS] showed that the escaping set of every entire function f contains unbounded connected sets. The”