Symbolic representations of iterated maps

Xin-Chu Fu, Weiping Lu, Peter Ashwin, Janiqiao Duan

DOI: http://dx.doi.org/10.12775/TMNA.2001.027

Abstract


This paper presents a general and systematic discussion of
various symbolic representations of iterated maps through subshifts.
A unified model for all continuous maps on a metric space is given.
It is shown that at most the second order
representation is enough for a continuous map.
By introducing distillations, partial representations
of some general continuous maps are obtained. Finally, partitions and
representations of a class of discontinuous maps and some examples
are discussed.

Keywords


Continuous map; discontinuous map; representation; subshift; symbolic dynamics

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