Symbolic dynamics and representations | Zendy

Valérie Berthé | Zendy

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Symbolic dynamics and representations

Author(s) -

Valérie Berthé

Publication year - 2017

Publication title -

les cours du cirm

Language(s) - English

Resource type - Journals

ISSN - 2108-7164

DOI - 10.5802/ccirm.24

Subject(s) - symbolic dynamics , symbolic computation , dynamical systems theory , the symbolic , focus (optics) , discretization , computation , object (grammar) , symbolic data analysis , partition (number theory) , theoretical computer science , algebra over a field , dynamical system (definition) , symbolic trajectory evaluation , computer science , dynamics (music) , mathematics , pure mathematics , artificial intelligence , algorithm , mathematical analysis , physics , psychology , quantum mechanics , combinatorics , acoustics , psychoanalysis , optics , model checking

The object of study of symbolic dynamics are discrete dynamical systems made of infinite sequences of symbols, with the shift acting on them. They come as codings of trajectories of points in a dynamical system according to a given partition. They are used as discretization tools for analyzing such trajectories, but they also occur in a natural way in arithmetics for instance. We first will recall basic definitions concerning symbolic dynamics and illustrate them with transformations like beta-numeration and continued fractions. We then focus on orbits that are relevant in computer science, namely finite and periodic ones, together by alluding to numerical issues for the computation of orbits.

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