Ergodic theory

branch of mathematics that studies dynamical systems

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In mathematics, ergodicity expresses the idea that a point of a moving system, either a dynamical system or a stochastic process, will eventually visit all parts of the space in which the system moves, in a uniform and random sense. This implies that the average behavior of the system can be deduced from the trajectory of a "typical" point. Equivalently, a sufficiently large collection of random samples from a process can represent the average statistical properties of the entire process. Ergodicity is a property of the system; it is a statement that the system cannot be reduced or factored in

hypothesis that typical physical systems studied in statistical mechanics are ergodic, such that time averages equal phase space averages

subset of a space acted upon by a group, which contains exactly one point from each of the orbits

generalization of the Bernoulli process to more than two possible outcomes

Integer multiples of many irrational mod 1 are uniformly distributed on the circle

apparent paradox in chaos theory that many complicated enough physical systems exhibited almost exactly periodic behavior instead of ergodic behavior

particular type of stochastic processes

nonnegative extended real number that is a measure of the complexity of a topological dynamical system

type of number sequence

Indian mathematician

system with no friction or other mechanism to dissipate the dynamics, such that the phase space does not shrink over time

mathematical description of thermodynamic mixing

field in the intersection of number theory, combinatorics, ergodic theory and harmonic analysis

a class of dynamical systems

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