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This article is cited in 1 scientific paper (total in 1 paper)
Geometry and real-analytic integrability
L. T. Butler School of Mathematics,
The University of Edinburgh,
6214 James Clerk Maxwell Building,
Edinburgh, UK, EH9 3JZ
Abstract:
This note constructs a compact, real-analytic, riemannian 4-manifold ($\Sigma, g$) with the properties that: (1) its geodesic flow is completely integrable with smooth but not real-analytic integrals; (2) $\Sigma$ is diffeomorphic to $\mathbf{T}^2 \times \mathbf{S}^2$; 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.
Received: 20.03.2006 Accepted: 29.06.2006
Citation:
L. T. Butler, “Geometry and real-analytic integrability”, Regul. Chaotic Dyn., 11:3 (2006), 363–369
Linking options:
https://www.mathnet.ru/eng/rcd682 https://www.mathnet.ru/eng/rcd/v11/i3/p363
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