Fletcher, Alastair N.
M.S. (Master of Science)
Department of Mathematical Sciences
Eremenko’s Conjecture is a long-standing problem in complex dynamics that asks whetherevery connected component of the set of escaping points of a transcendental entire function is unbounded. It was finally proven false in a paper by Mart ́ı-Pete, Lasse Rempe, and James Waterman that constructs a counterexample to the conjecture. This thesis seeks to pro- vide a background on Eremenko’s Conjecture, discuss the partial results surrounding it, and explain the construction of the counterexample in Mart ́ı-Pete, et al.’s paper.
Low, Paradise, "Counterexample to Eremenko's Conjecture" (2022). Graduate Research Theses & Dissertations. 7378.
Northern Illinois University
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