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2013
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L. Butler

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

Publications:

 Butler L. T. Geometry and real-analytic integrability 2006, vol. 11, no. 3, pp.  363-369 Abstract 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