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Slow-growing counterexamples to the strong Eremenko Conjecture

By Andrew Brown
Let \(f\colon\mathbb{C} \to\mathbb{C}\) be a transcendental entire function. In 1989, Eremenko asked the following question concerning the set \(I(f)\) of points that tend to infinity under iteration: can every point of \(I(f)\) be joined to \(\infty\) by a curve in \(I(f)\)? This is known as the strong Eremenko conjecture and... Show more
May 14, 2024
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