### Symbolic representations of iterated maps

#### 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.

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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