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Some open billiards with distinct top Lyapunov exponents
We study open billiard flows in $\mathbb{R}^3$ generated by reflections in the exterior of at least three ellipsoids with $C^3$ boundaries. Each obstacle is congruent to $$\tilde{K} = \{(x,y,z)\in \mathbb{R}^3 : x^2+y^2+(βz)^2 \leq r^2\},$$ with parameter $β>1$, small radii, and centers $O_i$ lying
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