本文摘要叙述有关三维紧致光滑流形上结构稳定的微分同胚的一个特征性定理的证明。

This note takes a sketch of a proof of a characterization theorem for diffeomorphisms oa a compact 3-dimensional smooth manifold to be structurally stable.

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本文给出了光滑流形上扩散过程耦合算子的一般形式，并证明了一类耦合具有耦合的基本性质。

This paper presents a general form of coupling operators for diffusion processes on smooth manifolds, and proves the basic coupling property for a class of couplings.

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我们证明了存在经济空间的一个稠密开子集，使得对开子集的每个点，都存在着均衡点，并且均衡商品价格包含一个H-1维光滑流形，这里H是事件树中顶点的数目。

Also we show that for an open, dense set of economies, the set of equilibrium prices contains a smooth II-1 dimensional manifold, where H is the numb…

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