从遍历观点看哈密顿回路
Hamiltonian loops from the ergodic point of view
摘要：
本文提供了遍历论和辛拓扑之间的联系。遍历论的一个经典概念是与变换群中的循环相关联的斜积映射。本文研究了辛流形上的Hamilton环同态群中的环的斜积。我们的主要问题是哪些同伦类的循环可以表示为严格遍历斜积。我们证明了一个存在性结果，并找到了一个障碍，这是由Hynn的几何上的哈密顿同构群。
英文摘要：
The paper provides a link between ergodic theory and symplectic topology. A classical notion of ergodic theory is a skew product map associated with a loop in a group of transformations. We study skew products which come from loops in the group of Hamiltonian diffeomorphisms of a symplectic manifold. Our main question is which homotopy classes of loops can be represented by strictly ergodic skew products. We prove an existence result, and find an obstruction which arises from Hofer's geometry on the group of Hamiltonian diffeomorphisms.
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