ergodisk
Ergodisk is a coined term used in discussions of ergodic theory to describe a disk-shaped dynamical system that exhibits ergodic behavior. In this usage, an ergodisk consists of a closed unit disk D in the plane equipped with a probability measure μ on its Borel sets and a μ-measurable map T: D → D that preserves μ.
Such a triple (D, μ, T) is called an ergodisk when T is ergodic with respect to μ, meaning
Concrete constructions of an ergodisk typically involve maps that mix the angular and radial coordinates in
Relation to other concepts: an ergodisk is a specific instance of a measure-preserving dynamical system on
See also: ergodic theory; measure-preserving transformation; ergodicity; Birkhoff's theorem; dynamical system.
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