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arXiv · 1710.01279

Geometry and Real-Analytic Integrability

Leo T. Butler
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Abstract

This note constructs a compact, real-analytic, riemannian 4-manifold (Σ, g) with the properties that: (1) its geodesic flow is completely integrable with smooth but not real-analytic integrals; (2) Σ is diffeomorphic to $T^2 \times S^2$ ; and (3) the limit set of the geodesic flow on the universal cover is dense. This shows there are obstructions to realanalytic integrability beyond the topology of the configuration space.

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Leo T. Butler. 2017-10-03. Geometry and Real-Analytic Integrability. https://doi.org/10.1070/rd2006v011n03abeh000359

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