In mathematics, ergodic flows occur in geometry, through the geodesic and horocycle flows of closed hyperbolic surfaces. Both of these examples have been...

In mathematics, ergodicity expresses the idea that a point of a moving system, either a dynamical system or a stochastic process, will eventually visit...

Ergodic theory is a branch of mathematics that studies statistical properties of deterministic dynamical systems; it is the study of ergodicity. In this...

In physics and thermodynamics, the ergodic hypothesis says that, over long periods of time, the time spent by a system in some region of the phase space...

and occur in the study of ergodic dynamical systems. The most celebrated of these is perhaps the Bernoulli flow. A flow on a set X is a group action...

flows need not be topologically transitive. Also, it is unknown if every C 1 {\displaystyle C^{1}} volume-preserving Anosov diffeomorphism is ergodic...

divided by the ergodic flow out of S {\displaystyle S} . Alistair Sinclair showed that conductance is closely tied to mixing time in ergodic reversible Markov...

becomes possible to classify the ergodic properties of Φ t. In using the Koopman approach of considering the action of the flow on an observable function, the...

classical phase space. This is consistent with the intuition that the flows of ergodic systems are equidistributed in phase space. By contrast, classical...

including Markov chains and subshifts of finite type, Anosov flows and Sinai's billiards, ergodic automorphisms of the n-torus, and the continued fraction...

Neumann, motivated by his study of single operators, group representations, ergodic theory and quantum mechanics. His double commutant theorem shows that the...

action restricts to an ergodic action of the reals on its centre, an Abelian von Neumann algebra. This ergodic flow is called the flow of weights; it is independent...

implies ergodicity: that is, every system that is weakly mixing is also ergodic (and so one says that mixing is a "stronger" condition than ergodicity). The...

(that an orbit, once having left an invariant subset, does not return). Ergodic flow Smale, S. (1967), "Differentiable Dynamical Systems", Bull. Amer. Math...

Cybertext as defined by Espen Aarseth in 1997 is a type of ergodic literature where the user traverses the text by doing nontrivial work. Cybertexts are...

dynamical systemsPages displaying short descriptions of redirect targets Ergodic theory – Branch of mathematics that studies dynamical systems List of topologies –...

object of study in the abstract formulation of dynamical systems, and ergodic theory in particular. Measure-preserving systems obey the Poincaré recurrence...

to a finite volume. The theorem is commonly discussed in the context of ergodic theory, dynamical systems and statistical mechanics. Systems to which the...

Romanian-American mathematician, who has made contributions to the fields of ergodic theory, probability and analysis. Bellow was born in Bucharest, Romania...

general, one cannot rule out "ergodic" flows (which basically means that an orbit is dense in some open set), or "subergodic" flows (which an orbit dense in...

so the dissipative parts agree. Hence the conservative parts agree. Ergodic flow Krengel 1985, pp. 16–17 Krengel 1985, pp. 17–18 Krengel 1985, p. 18 Krengel...

Własności ergodyczne gładkich potoków na powierzchniach (Ergodic properties of smooth flows on surfaces) and awarded the International Stefan Banach Prize...

IIIλ (0 ≤ λ ≤ 1) with the additional invariant of an ergodic flow on a Lebesgue space (the "flow of weights") when λ = 0. The JBW factor of Type I1 is...

screw lines. For some other values of the parameters, however, these flows are ergodic and particle trajectories are everywhere dense. The last result is...

or more generally when Γ {\displaystyle \Gamma } is a lattice, this flow is ergodic (with respect to the normalised Liouville measure). Moreover, in this...

his work on lattices in Lie groups, and the introduction of methods from ergodic theory into diophantine approximation. He was awarded a Fields Medal in...

Vol. 149, 1970, pp. 453–464. doi:10.1090/S0002-9947-1970-0259068-3 On ergodic flows and the isomorphism of factors, Mathematical Annals, Vol. 223, 1976...

relationship to other branches of mathematics, especially dynamical systems, ergodic theory, and number theory, as well as Riemann surfaces themselves. These...

systems, and in particular are the objects of study in symbolic dynamics and ergodic theory. They also describe the set of all possible sequences executed by...

involve small divisors. Stability of the Solar System Arnold diffusion Ergodic theory Hofstadter's butterfly Nekhoroshev estimates A. N. Kolmogorov, "On...