symbolic dynamics

In mathematics, symbolic dynamics is the practice of modelling a dynamical system 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 http://en.wikipedia.org/wiki/Symbolic_dynamicsSymbolic dynamics as of December 19, 2006.

单词	SymbolicDynamics
释义	symbolic dynamics In mathematics, symbolic dynamics is the practice of modelling a dynamical system 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 http://en.wikipedia.org/wiki/Symbolic_dynamicsSymbolic dynamics as of December 19, 2006.
随便看	some theorem schemas of intuitionistic propositional logic SomeTheoremSchemasOfNormalModalLogic some theorem schemas of normal modal logic SomeTheoremSchemasOfPropositionalLogic some theorem schemas of propositional logic SomeTheoremsOnStrictBetweennessRelations some theorems on strict betweenness relations SomeTheoremsOnTheAxiomsOfOrder some theorems on the axioms of order SomethingRelatedToAlexandrovOnepointCompactification something related to Alexandrov one-point compactification SomeValidSchemasOfFirstOrderLogic some valid schemas of first order logic SomeValuesCharacterisingI some values characterising i SophieGermain Sophie Germain SophieGermainPrime Sophie Germain prime SophomoresDream Sophomore’s dream SorgenfreyHalfopenPlane Sorgenfrey half-open plane SorgenfreyLine Sorgenfrey line