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 ?
All of the intravesical recurrence occurred within 18 months after surgery and the mean recurrence time was 8.
This indicates that the operation mode has no influence on the intravesical recurrence time.
Amiodarone (200mg/day) or sotalol (160 mg/day) were prescribed to all patients until to the 1st AF recurrence time (in AF recurrent group) or during the whole study period (in sinus rhythm group).
In addition to its long recurrence time, the segment is unusual in that it is longer than the rupture lengths of other earthquakes in the region.
1] In one study comparing ileal conduits to neobladders, average recurrence time was 2 years and no significant difference was found between the 2 groups.
Data from USC suggested that symptomatic presentation occurred later, with a median recurrence time of 30.
with energy magnitudes in excess of 9 [and] with recurrence times of greater than 400 years cannot be ruled out.