Poincaré recurrence theorem

(redirected from Poincare's recurrence theorem)

Poincaré recurrence theorem

[‚pwän‚kä′rā ri′kə·rəns ‚thir·əm]
(mathematics)
A volume preserving homeomorphism T of a finite dimensional Euclidean space will have, for almost all points x, infinitely many points of the form T i (x), i = 1, 2, … within any open set containing x.
A measure preserving transformation on a space with finite measure is recurrent.
References in periodicals archive ?
The former have the seemingly more devastating difficulty of dealing with Poincare's recurrence theorem and Loschmidt's reversibility objection.