 00487 XinChu Fu, Weiping Lu, Peter Ashwin and Jinqiao Duan
 Symbolic Representations of Iterated Maps
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Dec 5, 00

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Abstract. This paper presents a general and systematic discussion of
various symbolic representations of iterated maps through subshifts.
We give a unified model for all continuous maps on a metric space,
by representing
a map through a general subshift over usually an uncountable alphabet.
It is shown that at most the second order representation
is enough for a continuous map.
In particular, it is shown that the dynamics of onedimensional
continuous maps to a great extent can be transformed to
the study of subshift structure of a general symbolic
dynamics system. By introducing distillations, partial representations
of some general continuous maps are obtained.
Finally, partitions and representations of a class of discontinuous maps,
piecewise continuous maps are discussed, and as examples, a representation
of the Gauss map via a full shift over a countable alphabet and
representations of interval exchange transformations as subshifts of infinite
type are given.
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