# Hyperbolic entire functions and the Eremenko–Lyubich class: Class $$\mathcal {B}$$B or not class $$\mathcal {B}$$B?

@article{RempeGillen2017HyperbolicEF, title={Hyperbolic entire functions and the Eremenko–Lyubich class: Class \$\$\mathcal \{B\}\$\$B or not class \$\$\mathcal \{B\}\$\$B?}, author={Lasse Rempe-Gillen and Dave Sixsmith}, journal={Mathematische Zeitschrift}, year={2017}, volume={286}, pages={783-800} }

Hyperbolicity plays an important role in the study of dynamical systems, and is a key concept in the iteration of rational functions of one complex variable. Hyperbolic systems have also been considered in the study of transcendental entire functions. There does not appear to be an agreed definition of the concept in this context, due to complications arising from the non-compactness of the phase space. In this article, we consider a natural definition of hyperbolicity that requires expanding… CONTINUE READING

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