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# dynamical system

A mathematical formalization for any fixed "rule" which describes the time dependence of a points position in its ambient space.

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• Dynamical system — This article is about the general aspects of dynamical systems. For technical details, see Dynamical system (definition). For the study, see Dynamical systems theory. Dynamical redirects here. For other uses, see Dynamics (disambiguation). The… …   Wikipedia

• dynamical system — noun (physics) a phase space together with a transformation of that space • Topics: ↑physics, ↑natural philosophy • Hypernyms: ↑phase space • Hyponyms: ↑chaos …   Useful english dictionary

• Dynamical system (definition) — This article presents the many ways to define a dynamical system. See the main article, dynamical system, for an overview of the topic. The dynamical system concept is a mathematical formalization for any fixed rule which describes the time… …   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

• Random dynamical system — In mathematics, a random dynamical system is a measure theoretic formulation of a dynamical system with an element of randomness , such as the dynamics of solutions to a stochastic differential equation. It consists of a base flow, the noise ,… …   Wikipedia

• Projected dynamical system — Projected dynamical systems is a mathematical theory investigating the behaviour of dynamical systems where solutions are restricted to a constraint set. The discipline shares connections to and applications with both the static world of… …   Wikipedia

• Hadamard's dynamical system — In physics and mathematics, the Hadamard dynamical system or Hadamard s billiards is a chaotic dynamical system, a type of dynamical billiards. Introduced by Jacques Hadamard in 1898 [J. Hadamard, Les surfaces à courbures opposées et leurs lignes …   Wikipedia

• Linear dynamical system — In a linear dynamical system, the variation of a state vector (an N dimensional vector denoted mathbf{x}) equals a constant matrix(denoted mathbf{A}) multiplied by mathbf{x}. This variation can take two forms: either as a flow, in which mathbf{x} …   Wikipedia

• Liouville dynamical system — In classical mechanics, a Liouville dynamical system is an exactly soluble dynamical system in which the kinetic energy T and potential energy V can be expressed in terms of the s generalized coordinates q as followscite journal | last =… …   Wikipedia

• State space (dynamical system) — In the theory of discrete dynamical systems, a state space is a directed graph where each possible state of a dynamical system is represented by a vertex, and there is a directed edge from a to b if and only if ƒ(a) = b where the… …   Wikipedia