• measure-preserving dynamical system is an object of study in the abstract formulation of dynamical systems, and ergodic theory in particular. Measure-preserving...
    23 KB (3,592 words) - 13:02, 9 August 2024
  • Ergodicity (redirect from Ergodic measure)
    formal definitions of measure theory and dynamical systems, and rather specifically on the notion of a measure-preserving dynamical system. The origins of ergodicity...
    55 KB (8,917 words) - 13:22, 8 December 2024
  • reasonable example of a conservative system and more precisely, a measure-preserving dynamical system. It is measure-preserving, as the number of particles in...
    12 KB (1,808 words) - 02:58, 25 November 2023
  • Thumbnail for Markov chain
    a stationary distribution, then it can be converted to a measure-preserving dynamical system: Let the probability space be Ω = Σ N {\displaystyle \Omega...
    94 KB (12,750 words) - 22:22, 19 December 2024
  • Krylov–Bogolyubov theorem Krylov-Bogoliubov averaging method Measure-preserving dynamical system Ergodic theory Mixing (mathematics) Almost periodic function...
    5 KB (413 words) - 21:49, 5 November 2024
  • operator. Measure-preserving dynamical system Normalizing flow Optimal transport Theorem 3.6.1 in Bogachev 2007 Bogachev, Vladimir I. (2007), Measure Theory...
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  • Thumbnail for Mixing (mathematics)
    in ergodic theory—the study of stochastic processes and measure-preserving dynamical systems. Several different definitions for mixing exist, including...
    26 KB (4,728 words) - 23:25, 17 September 2024
  • Liouville's theorem (Hamiltonian) (category Theorems in dynamical systems)
    interpreted as positions and momenta; not all measure-preserving dynamical systems have these, but Hamiltonian systems do. The general setting for conjugate position...
    24 KB (3,887 words) - 18:56, 7 July 2024
  • In the mathematical field of dynamical systems, a random dynamical system is a dynamical system in which the equations of motion have an element of randomness...
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  • Thumbnail for Dynamical system
    class of systems it is always possible to construct a measure so as to make the evolution rule of the dynamical system a measure-preserving transformation...
    53 KB (7,150 words) - 18:46, 14 October 2024