symbolic dynamics

In mathematics, symbolic dynamicsMathworldPlanetmath is the practice of modelling a dynamical systemMathworldPlanetmathPlanetmath by a space consisting of infinite sequences of abstract symbols, each symbol corresponding to a state of the system, and a shift operator corresponding to the dynamics. Symbolic dynamics was first introduced by Emil Artin in 1924, in the study of Artin billiards.

Symbolic dynamics originated as a method to study general dynamical systems, but its techniques and ideas have found significant applications in data storage and transmission, linear algebra, the motions of the planets and many other areas. The distinct feature in symbolic dynamics is that time is measured in discrete intervals. So at each time interval the system is in a particular state. Each state is associated with a symbol and the evolution of the system is described by an infinite sequence of symbols - represented effectively as strings. If the system states are not inherently discrete, then the state vector must be discretized, so as to get a coarse-grained description of the system.

This entry was adapted from the Wikipedia article dynamics as of December 19, 2006.

Title symbolic dynamics
Canonical name SymbolicDynamics
Date of creation 2013-03-22 16:28:29
Last modified on 2013-03-22 16:28:29
Owner PrimeFan (13766)
Last modified by PrimeFan (13766)
Numerical id 5
Author PrimeFan (13766)
Entry type Definition
Classification msc 37-00