Poincaré recurrence theorem
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Poincaré recurrence theorem[‚pwän‚kä′rā ri′kə·rəns ‚thir·əm]
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.