Poincaré recurrence theorem [´pwän´kä`rā ri`kǝ·rǝns ´thir·ǝm] MATHEMATICS 1. A volume preserving homeomorphism T of a finite dimensional euclidean space will have, for almost all points x, infinitely many points of the form Ti(x ), i = 1, 2, ... within any open set containing x. 2. A measure preserving transformation on a space with finite measure is recurrent. |