Jian, Cheng, Surface Billiards and Nonvanishing Lyapunov Exponents, Acta Mathematica Sinica, New Series Chinese Journal of Mathematics, 13(1), 1997, pp. 21-34
We study in thi paper the billliards on surfaces with max-valued Gaussian curvature and the condition which gives nonvashing Lyaounov exponents of the system. We introduce a criterion upon which a small perturbation of surface will also produce a system with positive Lyapunov exponents. Some examples of such surfaces are given in this article.