On the frequency of recurrence

R. F. Shaimuratov

M. V. Lomonosov Moscow State University

Abstract: For sets with finite measure, the frequency of recurrence is shown to be positive. In the event of infinite measure, an example with zero frequency of recurrence is presented. The paper provides a sufficient condition under which the frequency of recurrence is not separated from zero.

Keywords: ergodic theory, Poincaré recurrence theorem, frequency of recurrence.

UDC: 519.21