Poincaré recurrence theorem

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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 goal is to investigate the relationship of the DKE theory developed here with the microscopic reversibility principle and the Poincare recurrence theorem. Finally in Section 5 the conclusions of the paper are drawn and possible applications/developments of the theory are pointed out.
probed the theory using the Poincare recurrence theorem. Nevertheless, the theorem is insufficient for predicting the time for a system to return, that is, the recurrence.
The next two statements are immediate consequences of the Poincare recurrence theorem.