0.0, -0.0000000);  ### 0-elliptic periodic trajectories {#elliptic-periodic-trajectories-0 .unnumbered}  There is a $0$-elliptic periodic trajectory without being $0$-periodic of the billiard within [eq:ellipse]{}, with a non-degenerate caustic ${\pazocal{C}}_{\gamma}$ if and only if, according to Theorem \[th:elliptic-cayley\]