## Journals

- Advances in Mathematics of Communications
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DCDS

We study the exponential rate of decay of Lebesgue numbers of open
covers in topological dynamical systems. We show that topological
entropy is bounded by this rate multiplied
by dimension. Some
corollaries and examples are discussed.

keywords:
Lipschitz constant
,
topological entropy
,
exponential decay.
,
open cover
,
box dimension
,
Lebesgue number
,
Hausdorff dimension

DCDS

In this paper we study a skew product map $F$ preserving an ergodic measure $\mu$
of positive entropy.
We show that if on the fibers the map are $C^{1+\alpha}$ diffeomorphisms with
nonzero Lyapunov exponents, then $F$ has ergodic measures of arbitrary intermediate entropies. To construct these measures
we find a set on which the return map is a skew product with horseshoes
along fibers. We can control the average return time and show the maximal
entropy of these measures can be arbitrarily close to $h_\mu(F)$.

keywords:
skew product
,
ergodic measure
,
Pesin theory.
,
entropy
,
return map
,
Lyapunov exponents
,
horseshoe

## Year of publication

## Related Authors

## Related Keywords

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