| dc.description.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 one-dimensional 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. | en_GB |
