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.
關聯:
TAIWANESE JOURNAL OF MATHEMATICS Volume: 12 Issue: 7 Pages: 1791-1803
