  Area and orientation preserving diffeomorphisms of the standard 2-disc,
referred to as symplectomorphisms of $\mathbb{D}^{2}$, allow decompositions in
terms of positive twist diffeomorphisms. Using the latter decomposition we
utilize the Conley index theory of discrete braid classes as introduced in
[Ghrist et al., C. R. Acad. Sci. Paris S\'er. I Math., 331(11), 2000, Invent.
Math., 152(2), 2003] in order to obtain a Morse type forcing theory of periodic
points: a priori information about periodic points determines a mapping class
which may force additional periodic points.
