TITLE

On the relation between topological entropy and entropy dimension

AUTHOR(S)
Saltykov, P. S.
PUB. DATE
June 2009
SOURCE
Mathematical Notes;Jun2009, Vol. 86 Issue 1/2, p255
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
For the Lipschitz mapping of a metric compact set into itself, there is a classical upper bound on topological entropy, namely, the product of the entropy dimension of the compact set by the logarithm of the Lipschitz constant. The Ghys conjecture is that, by varying the metric, one can approximate the upper bound arbitrarily closely to the exact value of the topological entropy. In the present paper, we obtain a criterion for the validity of the Ghys conjecture for an individual mapping. Applying this criterion, we prove the Ghys conjecture for hyperbolic mappings.
ACCESSION #
44312880

 

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