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...

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

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

T {\displaystyle T} is a measure preserving dynamical system in this case, otherwise, it is merely a conservative system. The term Bernoulli sequence...

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...

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...

the notion of entropy in statistical mechanics. In dynamical systems, statistical complexity measures the size of the minimum program able to statistically...

{\displaystyle \left(T,X,{\mathcal {B}}(X),\mu \right)} is a measure-preserving dynamical system. It has also been proved that the above are equivalent to...

Authalic latitude Authalic radius Equiareal map (mathematics) Measure-preserving dynamical system Geodesic polygon area Snyder, John P. (1987). Map projections...

aperiodic measure preserving dynamical system can be decomposed to an arbitrary high tower of measurable sets and a remainder of arbitrarily small measure. It...

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

isomorphic to Bernoulli shifts, and gave criteria for a given measure-preserving dynamical system to be isomorphic to a Bernoulli shift. A corollary of these...

random dynamical system is a dynamical system in which the equations of motion have an element of randomness to them. Random dynamical systems are characterized...

meaningless. Also see ergodic theory and ergodic process. Measure-preserving dynamical system Peebles, P. Z., 2001, Probability, Random Variables and Random...

spectral quantities of the Koopman operators for general measure-preserving dynamical systems. This method employs an orthogonal Procrustes problem (essentially...

several different measures, thus leading to a measure-preserving dynamical system. A common object of study is the Markov measure, which is an extension...

the study of invariant measures in dynamical systems. The Krylov–Bogolyubov theorem proves the existence of invariant measures under certain conditions...

structures and deeper symbolic architectures. Measure-preserving dynamical system Combinatorics and dynamical systems Shift space Shift of finite type Complex...

μ , T ) {\displaystyle (X,{\mathcal {A}},\mu ,T)} is a measure-preserving dynamical system, and is called a Bernoulli scheme or a Bernoulli shift. It...

has also given a deeper understanding of the structure of measure-preserving dynamical systems. Szemerédi's theorem is a result in arithmetic combinatorics...

p {\displaystyle L^{p}} spaces Measure-preserving dynamical system – Subject of study in ergodic theory Vector measure Weakly measurable function Strichartz...

proof was presented by Constantin Carathéodory using measure theory in 1919. Any dynamical system defined by an ordinary differential equation determines...

dissipation, as commonly used in the mathematical study of measure-preserving dynamical systems, is given in the article wandering set. Dissipation is the...

S2CID 205317873. Salerno, Grazia; Carusotto, Iacopo (2014). "Dynamical decoupling and dynamical isolation in temporally modulated coupled pendulums". EPL...

mathematics that studies statistical properties of deterministic dynamical systems; it is the study of ergodicity. In this context, "statistical properties"...

k^{-m}<1} that marks this as a dissipative system: for a non-dissipative measure-preserving dynamical system, the eigenvalues of the transfer operator...

stability of solutions of differential equations and of trajectories of dynamical systems under small perturbations of initial conditions. The heat equation...