关于特征指数:一个新的为向量场乘法遍历定理而构造的Borel集

On Characteristic Exponents Construction of a New Borel Set for the Multiplicative Ergodic Theorem for Vector Fields

设在一紧致光滑流形上任给定一C^1切向量场S。本文提出一个满足对于S来说的乘法遍历定理的需要的Borel集。比起以往文献上为同样目的曾经出现过的集合来说,现在这集合较有限制些;但同时由于它在其构造中呈限出以往不曾有过的新属性(例如,可参看V.I.Oseledec,A.Katok-J.Strelcyn, A.Fathi-M.Hereman-J.Yoccoz,D.Ruelle,R.Johnson-K.Palmer-C.Sell,R.Ma…等人的有关工作),因而也可能更有用些。这样的应用将见作者以后的文章中。

We present in the paper a Borel subset of a compact smooth manifold Ma to satisfy the requirements of the multiplicative ergodic theorem for a C1 tangent vector field on M(?). This set is more restrictive but might be more useful than other ones for the same purpose appearing previously in the literature.