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dynamical theorem

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  • 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

  • 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 (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

  • List of dynamical systems and differential equations topics — This is a list of dynamical system and differential equation topics, by Wikipedia page. See also list of partial differential equation topics, list of equations. Contents 1 Dynamical systems, in general 2 Abstract dynamical systems 3 …   Wikipedia

  • Oseledets theorem — In mathematics, the multiplicative ergodic theorem, or Oseledets theorem provides the theoretical background for computation of Lyapunov exponents of a nonlinear dynamical system. It was proved by Valery Oseledets (also spelled Oseledec ) in 1965 …   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

  • Takens' theorem — In mathematics, a delay embedding theorem gives the conditions under which a chaotic dynamical system can be reconstructed from a sequence of observations of the state of a dynamical system. The reconstruction preserves the properties of the… …   Wikipedia

  • Poincaré–Bendixson theorem — In mathematics, the Poincaré–Bendixson theorem is a statement about the long term behaviour of orbits of continuous dynamical systems on the plane. Overview The Poincaré–Bendixson theorem states that any orbit which stays in a compact region of… …   Wikipedia

  • Perron–Frobenius theorem — In linear algebra, the Perron–Frobenius theorem, proved by Oskar Perron (1907) and Georg Frobenius (1912), asserts that a real square matrix with positive entries has a unique largest real eigenvalue and that the corresponding… …   Wikipedia

  • Poincaré recurrence theorem — In mathematics, the Poincaré recurrence theorem states that certain systems will, after a sufficiently long time, return to a state very close to the initial state. The Poincaré recurrence time is the length of time elapsed until the recurrence.… …   Wikipedia

  • Hartman-Grobman theorem — In mathematics, in the study of dynamical systems, the Hartman Grobman theorem or linearization theorem is an important theorem about the local behaviour of dynamical systems in the neighbourhood of a hyperbolic fixed point.Basically the theorem… …   Wikipedia

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