On a question of Eremenko concerning escaping components of entire functions
By Lasse Rempe. 2006
49 citations recorded by the source corpus.
Let f be an entire function with a bounded set of singular values, and suppose furthermore that the postsingular set of f is bounded. We show that every component of the escaping set I(f) is unbounded. This provides a partial answer to a question of Eremenko.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/e09daf7f572906a0a588252e054907f4d656e3d1
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In Applied Mathematics
- Lasse Rempe
- Walter Bergweiler
- G. Stallard
- P. Rippon
- Dierk Schleicher
- Günter Rottenfusser
- Johannes Ruckert
- Christopher J. Bishop
In Mathematical Physics
- Lasse Rempe
- Walter Bergweiler
- G. Stallard
- P. Rippon
- Dierk Schleicher
- Günter Rottenfusser
- Johannes Ruckert
- Christopher J. Bishop
Citations in the corpus
- Dynamic rays of bounded-type entire functions (2007, background): “Also, recently [ R1 ] the weak form of Eremenko’s conjecture was established for functions f ∈ B whose postsingular set is bounded (which applies, in particular, to the hyperbolic counterexample constructed in Theorem 1.1).”
- Dynamics of meromorphic functions with direct or logarithmic singularities (2007, background): “Since then the conjecture has also been proved for certain more general classes of entire functions by Barański [2], Rempe [31] and Rottenfußer, Rückert, Rempe and Schleicher [41].”
- Multiply connected wandering domains of entire functions (2011, background): “This set was introduced in [14] and has turned out to be important in the dynamics of entire functions; see [38, 44, 45], for example.”