On the sensitivity of additive cellular automata in Besicovitch topologies

We prove that additive cellular automata in the Besicovitch topology that have a Willson limit set of Hausdorff dimension strictly bigger than 1 are sensitive to initial conditions.

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Bibliographic Details
Published in:Theoretical computer science 2003-05, Vol.301 (1-3), p.341-354
Main Author: Formenti, Enrico
Format: Article
Language:English
Subjects:
Applied sciences
Automata. Abstract machines. Turing machines
Computer science
control theory
systems
Exact sciences and technology
Global analysis, analysis on manifolds
Mathematics
Sciences and techniques of general use
Theoretical computing
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
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Description
Summary:We prove that additive cellular automata in the Besicovitch topology that have a Willson limit set of Hausdorff dimension strictly bigger than 1 are sensitive to initial conditions.
ISSN:0304-3975
1879-2294
DOI:10.1016/S0304-3975(02)00591-1