Topological Entropy Ii: Homogeneous Measures

Book Id: WPLBN0000676035
Format Type: PDF eBook:
File Size: 0.2 MB
Reproduction Date: 2005

Title:	Topological Entropy Ii: Homogeneous Measures
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Language:	English
Subject:	Science., Mathematics, Logic
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Citation APA MLA Chicago Topological Entropy Ii: Homogeneous Measures. (n.d.). Topological Entropy Ii: Homogeneous Measures. Retrieved from http://self.gutenberg.org/

Description
Mathematics document containing theorems and formulas.

Excerpt
Excerpt: In this section we show how the topological entropy of simple examples may be computed explicitly, and then show that in good situations certain measure{ theoretic entropies may be deduced. A topological Kolmogorov {Sinai type theorem We have seen that if f ng is a sequence of open covers with diam( n) ! 0, then h(T) = limn!1 h(T; n). This is a topological analogue of Theorem 4.10. We now give a topological analogue of Theorem 4.6. Let X denote a compact metric space. A homeomorphism T : X ! X is expansive if there is an expansive constant > 0 with the property that if x 6= y then there is an n 2 Z with d(Tn; Tny) > . A finite open cover is a generator for T if for each map : Z ! , the set T1n = 1 T n ( n) contains at most one point of X. A finite open cover is a weak generator for T if for each map : Z ! , the set T1n = 1 T n (n) contains at most one point of X.