Annales Academię Scientiarum Fennicę
Mathematica
Volumen 36, 2011, 71-80

CONNECTED ESCAPING SETS OF EXPONENTIAL MAPS

Lasse Rempe

University of Liverpool, Department of Mathematical Sciences
Liverpool L69 7ZL, United Kingdom; l.rempe 'at' liverpool.ac.uk

Abstract. We show that, for many parameters a \in C, the set I(f_a) of points that converge to infinity under iteration of the exponential map f_a(z) = e^z + a is connected. This includes all parameters for which the singular value a escapes to infinity under iteration of f_a.

2000 Mathematics Subject Classification: Primary 37F10, 30D05.

Key words: Julia set, exponential map, Eremenko's Conjecture.

Reference to this article: L. Rempe: Connected escaping sets of exponential maps. Ann. Acad. Sci. Fenn. Math. 36 (2011), 71-80.

Full document as PDF file

doi:10.5186/aasfm.2011.3604

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