A counterexample to Eremenko's Conjecture

Abstract: I shall speak within my lecture

about an interesting conjecture

of Eremenko from a fine

paper of 1989.

>>>

He asked if each escaping point

can to infinity be joined

using a connected shape

all points of which themselves escape.

>>>

Although quite simple it appears,

this question has for many years

caused me and others some despair,

sleepless nights and greying hair.

>>>

Through our intense investigation

of transcendental iteration,

much progress was indeed obtained,

but the conjecture, it remained -

>>>

till now! By work with Waterman

and Martí-Pete, now I can

describe to you, within my lecture,

a counterexample to Eremenko's Conjecture.

complex variablesdynamical systems

Audience: researchers in the topic

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