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The exponential map is chaotic

Lasse Rempe

Palomar Registrypalomar/PALOMAR-2026-09-16-000001Sep 16, 2026math.DSscore 0

In 1926, Fatou conjectured that the Julia set of the complex exponential map is the entire complex plane; in other words, the dynamical system described by the map is unstable under perturbation at every point in the plane. Misiurewicz proved this conjecture in 1981. In 2015, Shen and Rempe published "The Exponential Map Is Chaotic: An Invitation to Transcendental Dynamics", giving an elementary and conceptual proof of Misiurewicz's theorem and deriving its dynamical consequences, without requiring advanced results from complex analysis or dynamics. This project formalises these results in…

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