Computable functions as Reeb flows

2026/07/10 by Kai Cieliebak, Ángel González-Prieto, Eva Miranda · 1 voice
Mathematics · Computer Science · #math.SG #cs.CC #math.DS

paper · pdf

Abstract

We prove that, given any contact 3-manifold and any computable function f: ℕ \dashrightarrow ℕ, there exists a defining contact form and a Poincaré section of its Reeb flow whose partially defined return map computes f.

Citations

• Topological Kleene Field Theories as a model of computation
• Proof of Hofer-Wysocki-Zehnder's two or infinity conjecture
• Hydrodynamic and symbolic models of computation with advice
• Constructing Turing complete Euler flows in dimension 3
• The Nature of Computation
• The Seiberg–Witten equations and the Weinstein conjecture
• On Non-Computable Functions
• Diffeomorphisms of the 2-sphere

Discussions

• Kai Cieliebak, \'Angel Gonz\'alez-Prieto, Eva Miranda: Computable functions as Reeb flows https://arxiv.org/abs/2607.10022 https://arxiv.org/pdf/2607.10022 https://arxiv.org/html/2607.10022 [bsky, 0 points, 0 comments]

Related

• Contact geometry and the Poincaré conjecture
• Reeb flows with small contact volume and large return time to a global section
• Perfect Reeb flows and action-index relations
• Contact homology and higher dimensional closing lemmas
• Contact Ricci flow