symbolic dynamics

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• Symbolic dynamics — In mathematics, symbolic dynamics is the practice of modelling a topological or smooth dynamical system by a discrete space consisting of infinite sequences of abstract symbols, each of which corresponds to a state of the system, with the… …   Wikipedia

• Dynamics — (from Greek δυναμικός dynamikos powerful , from δύναμις dynamis power ) may refer to: Contents 1 Physics and engineering 2 Sociology and psychology 3 Computer science and mathematics …   Wikipedia

• Nonlinear Dynamics (journal) — Nonlinear Dynamics, An International Journal of Nonlinear Dynamics and Chaos in Engineering Systems   …   Wikipedia

• Markov partition — A Markov partition is a tool used in dynamical systems theory, allowing the methods of symbolic dynamics to be applied to the study of hyperbolic systems. By using a Markov partition, the system can be made to resemble a discrete time Markov… …   Wikipedia

• Dynamical systems theory — is an area of applied mathematics used to describe the behavior of complex dynamical systems, usually by employing differential equations or difference equations. When differential equations are employed, the theory is called continuous dynamical …   Wikipedia

• Horseshoe map — In the mathematics of chaos theory, a horseshoe map is any member of a class of chaotic maps of the square into itself. It is a core example in the study of dynamical systems. The map was introduced by Smale while studying the behavior of the… …   Wikipedia

• Measure-preserving dynamical system — In mathematics, a measure preserving dynamical system is an object of study in the abstract formulation of dynamical systems, and ergodic theory in particular. Contents 1 Definition 2 Examples 3 Homomorphisms 4 …   Wikipedia

• Combinatorics and dynamical systems — The mathematical disciplines of combinatorics and dynamical systems interact in a number of ways. The ergodic theory of dynamical systems has recently been used to prove combinatorial theorems about number theory which has given rise to the field …   Wikipedia

• Shift space — In symbolic dynamics and related branches of mathematics, a shift space or subshift is a set of infinite words representing the evolution of a discrete system. In fact, shift spaces and symbolic dynamical systems are often considered synonyms.… …   Wikipedia

• Subshift of finite type — In mathematics, subshifts of finite type are used to model dynamical systems, and in particular are the objects of study in symbolic dynamics and ergodic theory. They also describe the set of all possible sequences executed by a finite state… …   Wikipedia

• Curtis–Hedlund–Lyndon theorem — The Curtis–Hedlund–Lyndon theorem is a mathematical characterization of cellular automata in terms of their symbolic dynamics. It is named after Morton L. Curtis, Gustav A. Hedlund, and Roger Lyndon; in his 1969 paper stating the theorem, Hedlund …   Wikipedia