A family of entire functions with Baker domains

Fleischmann, Dominique S. (2009). A family of entire functions with Baker domains. Ergodic Theory and Dynamical Systems, 29(2) pp. 495–514.

DOI: https://doi.org/10.1017/S0143385708080383

Abstract

In his paper [The iteration of polynomials and transcendental entire functions. J. Aust. Math. Soc. (Series A) 30 (1981), 483–495], Baker proved that the function f defined by f(z) = z+(sin?z/?z)+c has a Baker domain for c sufficiently large. In this paper we use a novel method to prove that f has a Baker domain for all c>0. We also prove that there exists an open unbounded set contained in the Baker domain on which the orbits of points under f are asymptotically horizontal.

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