Billiards in Cosmological Models

Recently the billiards, forming an important part in theory of dynamical systems with singularities [1,2], found their unexpected application in cosmological problems. It turnes out that a wide class of cosmological models near a singular point, corresponding to the origin of development of our Universe, admits its representation as billiards on the space of constant negative curvature [4,5]. A problem of similar model randomness is reduced to a problem of properties of corresponding billiards. The aim of the present paper is to show the way in which such representation is reached and to present the results obtained within the limits of those models.