ESTIMATE FOR SUPREMUM OF CONDITIONAL ENTROPY ON A CLOSED SUBSET

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Title:	ESTIMATE FOR SUPREMUM OF CONDITIONAL ENTROPY ON A CLOSED SUBSET
Authors:	Cheng, Wen-Chiao
Contributors:	應用數學系
Keywords:	Conditional metric entropy Topological entropy Variational inequality
Date:	2008
Issue Date:	2009-11-04 14:15:52 (UTC+8)
Abstract:	This paper compares the conditional metric entropy h(mu)(T vertical bar G), with the topological entropy, h(top)(T vertical bar G), of a continuous map T, where G is a closed fully T-invariant subset. The following Variational Inequality is proven, h(top)(T vertical bar G) <= sup(mu is an element of M(X,T)) h(mu)(T vertical bar < G >) <= h(top)(T vertical bar G) + h(top)(T vertical bar cl(X\G)) where M(X, T) is the collection of all invariant measures of X, which is an extension of the usual variational principle when G = X.
Relation:	TAIWANESE JOURNAL OF MATHEMATICS Volume: 12 Issue: 7 Pages: 1791-1803
Appears in Collections:	[Department of Applied Mathematics] journal articles

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