Dynamical Systems seminar - Constructing slow-growing counterexamples to the Strong Eremenko Conjecture

Dates

Wednesday, February 21, 2024 - 13:30 to 14:30

Speaker: Andrew Brown (University of Liverpool)

Abstract: The strong Eremenko Conjecture was disproved in the paper of Rottenfußer, Rückert, Rempe and Schleicher with a counterexample function in the Eremenko—Lyubich Class B with infinite order growth. It was also shown in the same paper that the conjecture holds for functions of finite order growth (and finite compositions of them). This talk will discuss the construction of counterexample functions with infinite order growth that grow asymptotically to finite order functions.