Symbolic Representations of Iterated Maps

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dc.creatorFu, Xin-Chu
dc.creatorLu, Weiping
dc.creatorAshwin, Peter
dc.creatorDuan, Jinqiao
dc.date2000-12-05
dc.date.accessioned2026-07-07T05:33:11Z
dc.date.available2026-07-07T05:33:11Z
dc.descriptionThis 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.
dc.identifierhttps://arxiv.org/abs/nlin/0012007
dc.identifierhttp://arxiv.org/abs/nlin/0012007
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/79911
dc.subjectChaotic Dynamics
dc.subjectMathematical Physics
dc.subjectDynamical Systems
dc.subjectRepresentation Theory
dc.subjectPattern Formation and Solitons
dc.titleSymbolic Representations of Iterated Maps
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