Symplectomorphisms and discrete braid invariants

Abstract

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 Sér. 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.

31 pages, in print in Journal of Fixed Point Theory and Applications