Two homoclinic classes conjecture for the periodic points $p_n$

Let $p_n$ be the periodic points of the billiard map, let $C_0$ and $C_1$ denote homoclinic classes, and let $a_n$, $b_n$, and $b_{17}$ be the parameters appearing in the paper. Two-class conjecture for $p_n$. The periodic points $p_n$ generate two homoclinic classes: $C_0$ is the homoclinic class of those $p_n$ with $n\leq16$ or $\lambda<a_n$, while $C_1$ is the homoclinic class of those $p_n$ with $n\geq17$ and $\lambda>b_n$. If $\lambda>b_{17}$, so that $C_1$ is nonempty, then

$$C_0\prec C_1.$$

This numerical conjecture describes the organization of the surviving periodic points into two homoclinic classes; the source gives no proof.