Chaotic Focusing Billiards in Higher Dimensions

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Abstract
Numerical computations of Lyapunov exponents for a class of three- and four-dimensional billiards whose boundary consists of flat and spherical components illustrate that such billiards are chaotic due to a defocusing mechanism similar to the one which produces chaos in two-dimensional billiards (e.g., in the stadium). These results demonstrate that recently established rigorous results or higher dimensional defocusing billiards are valid under substantially weaker assumptions.

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