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We study the nonautonomous discrete dynamical system ( NADDS, for
simplicity) given by a sequence \(\{f_n\}_{n=1}^{\infty}\) of
continuous self-maps of a compact metric space \(X\). Different
aspects of dynamics of NADDS (such as topological entropy,
measure-theoretical entropy, minimality) were studied in [2],
[5], [3].
We will describe a generalization of the
notion of local measure entropy, introduced by Brin and Katok
[1] for a single map, to NADDS.
Finally, we apply the theory of dimensional type characteristics of
a dynamical system, elaborated by Pesin [4], to obtain a
relationship between topological entropy of NADDS and its local
measure entropies. We intend to present NADDS-homogeneous measures
and recall some of their properties.
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References- M. Brin, A. Katok, On local entropy , in
Geometric Dynamics, Lecture Notes in Math., Vol. 1007, Springer,
Berlin (1983), 30-38.
- S. Kolyada, L. Snoha, Topological
entropy of nonautonomous dynamical systems , Random and
Computational Dynamics 4, 1996, 205-233.
- S. Kolyada, L.Snoha and S.Trofimchuk,
On minimality of nonautonomous dynamical systems , Nonlinear
Oscilations 7, 2004, 83-89.
- Ya. Pesin, Dimension Theory in
Dynamical Systems , Chicago Lectures in Mathematics, The
University of Chicago Press, Chicago, 1997.
- Y. Zhu, Z. Liu, W. Zhang, Entropy of
nonautonomous dynamical systems , J. Korean Math. Soc 49, 2012,
165-185.
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