Sfb 288 Differential Geometry and Quantum Physics

Abstract for Sfb Preprint No. 426

Integrable geodesic flows on the suspensions of toric automorphisms

A.V. Bolsinov and I.A. Taimanov

For any toric automorphism $A in SL(n,Z)$ with only real eigenvalues a Riemannian metric with an integrable geodesic flow on the suspension of this automorphism is constructed. A qualitative analysis of such a flow on a three-solvmanifold constructed by the authors in the previous work is done. This flow is an example of the geodesic flow, which has vanishing Liouville entropy and, moreover, is integrable but has positive topological entropy. The authors also discuss some open problems on integrability of geodesic flows and related subjects.

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