As pointed out in Hsu et al. [1988], the calculation of the invariant set is generally not very sensitive to the value of as long as 0 < < 1. We use = 1/2

Two algorithms that compute the manifolds are documented in You et al. [1991], one that uses a rigorous method and one that does not. Unfortunately, the rigorous algorithm requires information about the Jacobian of f, and since explicitly obtaining the Jacobian for the billiard system is very cumbersome, we only use the nonrigorous algorithm. On the other hand, it was shown in You et al. [1991] that pictures generated from the two algorithms are generally indistinguishable.

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