A homoclinic version of the central limit theorem

The definitions of homoclinic partitions and transformations are given in situations that are standard for topological dynamics and ergodic theory. A variant of the central limit theorem is proved, the formulation of which makes use of homoclinic transformations.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 184, pp. 80–91, 1990.