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On almost automorphic dynamics in symbolic lattices

Published online by Cambridge University Press:  04 May 2004

ARNO BERGER ,
STEFAN SIEGMUND  and
YINGFEI YI
ARNO BERGER
Affiliation:
Institute of Mechanics, Vienna University of Technology, A-1040 Vienna, Austria (e-mail: aberger@mch2ws1.mechanik.tuwien.ac.at)
STEFAN SIEGMUND
Affiliation:
Institute for Mathematics and its Applications, University of Minnesota, Minneapolis, MN 55455, USA (e-mail: siegmund@ima.umn.edu)
YINGFEI YI
Affiliation:
School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, USA (e-mail: yi@math.gatech.edu)
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Abstract

We study the existence, structure and topological entropy of almost automorphic arrays in symbolic lattice dynamical systems. In particular, we show that almost automorphic arrays with arbitrarily large entropy are typical in symbolic lattice dynamical systems. Applications to pattern formation and spatial chaos in infinite-dimensional lattice systems are considered and the construction of chaotic almost automorphic signals is discussed.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 24 , Issue 3 , June 2004 , pp. 677 - 696
Copyright
2004 Cambridge University Press

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