measure-preserving dynamical system is an object of study in the abstract formulation of dynamical systems, and ergodic theory in particular. Measure-preserving...

formal definitions of measure theory and dynamical systems, and rather specifically on the notion of a measure-preserving dynamical system. The origins of ergodicity...

reasonable example of a conservative system and more precisely, a measure-preserving dynamical system. It is measure-preserving, as the number of particles in...

a stationary distribution, then it can be converted to a measure-preserving dynamical system: Let the probability space be Ω = Σ N {\displaystyle \Omega...

Krylov–Bogolyubov theorem Krylov-Bogoliubov averaging method Measure-preserving dynamical system Ergodic theory Mixing (mathematics) Almost periodic function...

interpreted as positions and momenta; not all measure-preserving dynamical systems have these, but Hamiltonian systems do. The general setting for conjugate position...

operator. Measure-preserving dynamical system Normalizing flow Optimal transport Theorem 3.6.1 in Bogachev 2007 Bogachev, Vladimir I. (2007), Measure Theory...

in ergodic theory—the study of stochastic processes and measure-preserving dynamical systems. Several different definitions for mixing exist, including...

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...

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...