Stepanoff flows on the torus
Stepanoff flows on the torus
复制标题
环面上的斯捷潘诺夫流
DOI：
10.1090/s0002-9939-1953-0060812-4
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发表时间：
1953
期刊：
影响因子：
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通讯作者：
J. C. Oxtoby
中科院分区：
文献类型：
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作者：
J. C. Oxtoby
Saito [61] 最近发表的一篇论文中的一项声明提出了以下问题：环面上是否存在具有驻点的解析、保面积、遍历流？本说明的目的是描述此类流的基本示例，并讨论其所属的流的拓扑类的一些属性。 Stepanoff [7]（另参见[4, pp. 395-400, 506-507]）考虑了由形式（1）的方程定义的流，其中Y= aX，a是无理数，X是周期的、非负的、连续的，在x和y中满足Lipschitz条件，并且在环面的一个且仅一个点处消失。他证明这些流量相对于不变的 Borel 测度而言是度量传递的
A statement in a recent paper by Saito [61 suggested the following question: Does there exist on the torus an analytic, area preserving, ergodic flow which has a stationary point? The purpose of this note is to describe an elementary example of such a flow, and to discuss some properties of a topological class of flows to which it belongs. Stepanoff [7) (cf. also [4, pp. 395-400, 506-507]) considered the flows defined by equations of the form (1) where Y= aX, a is an irrational number, and X is periodic, non-negative, continuous, satisfies a Lipschitz condition in x and y, and vanishes at one and only one point of the torus. He showed that these flows are metrically transitive with respect to the invariant Borel measure