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L. Butler

The University of Edinburgh Centre, 7-11 Nicolson Street, EH8 9YL, Edinburgh
University of Edinburgh


Butler L. T.
Geometry and real-analytic integrability
2006, vol. 11, no. 3, pp.  363-369
This note constructs a compact, real-analytic, riemannian 4-manifold $(\sum, \mathscr{g})$ with the properties that: (1) its geodesic flow is completely integrable with smooth but not real-analytic integrals; (2) $\sum$ is diffeomorphic to ${\bf T}^2 \times {\bf S}^2$; and (3) the limit set of the geodesic flow on the universal cover is dense. This shows there are obstructions to real-analytic integrability beyond the topology of the configuration space.
Keywords: geodesic flows, integrable systems, momentum map, real-analytic integrability
Citation: Butler L. T.,  Geometry and real-analytic integrability , Regular and Chaotic Dynamics, 2006, vol. 11, no. 3, pp. 363-369
DOI: 10.1070/RD2006v011n03ABEH000359

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