An inequality for the entropy of differentiable maps
An inequality for the entropy of differentiable maps
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DOI：
10.1007/bf02584795
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发表时间：
1978-03
期刊：
影响因子：
--
通讯作者：
D. Ruelle
中科院分区：
文献类型：
--
作者：
D. Ruelle
本文的目的是证明下面的定理2，它给出了在紧致流形M到自身的可微映射f下任何概率测度p不变的测度论熵h（p）的上界。上界是由Oseledec [2]的非交换遍历定理引入的特征指数。我们首先制定一个版本的后一个定理将适合于我们的目的。
The purpose of this note is to prove Theorem 2 below, which gives an upper bound to the measure-theoretic entropy h (p) of any probability measure p invariant under a differentiable map f of a compact manifold M into itself. The upper bound is in terms of characteristic exponents introduced by the non-commutative ergodic theorem of Oseledec [2]. We first formulate a version of the latter theorem which will be suited to our purposes.