环面自同构悬置上的可积测地流
Integrable geodesic flows on the suspensions of toric automorphisms
摘要：
对任何只具有实特征值的环面自同构，构造了一个在其悬挂上具有可积测地流的黎曼度量。本文对作者在数学DG/9905078中构造的三解流形上的这类流动作了定性分析。这个流是测地流的一个例子，测地线流的刘维尔熵为零，而且是可积的，但具有正的拓扑熵。讨论了测地流的可积性及相关问题。
英文摘要：
For any toric automorphism 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 math.DG/9905078 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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