Geodesic
On billiards close to dispersing
Sbornik. Mathematics, Tome 23 (1974) no. 1, pp. 45-67

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One considers dynamical systems generated by billiards which are “perturbations” of dispersing billiards. It is shown that such dynamical systems are systems of A. N. Kolmogorov ($K$-systems), if the “perturbation” satisfies certain conditions which have an intuitive geometric interpretation. Bibliography: 12 titles. 
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L. A. Bunimovich. On billiards close to dispersing. Sbornik. Mathematics, Tome 23 (1974) no. 1, pp. 45-67. http://geodesic.mathdoc.fr/item/SM_1974_23_1_a2/