From semitoric systems to Floer theory and integrable dynamics.

Semitoric systems are a type of dynamical system (such as a spinning top) which satisfy certain symmetries. These systems can be well understood in terms of five invariants which can be recovered from the system. Semitoric systems lie in the field of symplectic geometry, another subfield of symplecitc geometry is Floer theory, which attempts to compute and understand certain invariants of symplectic manifolds and their Lagrangian submanifolds (a type of submanifold which arises naturally in the study of semitoric systems). We propose to (1) initiate research to better understand the invariants of semitoric systems (2) expand results and ideas from semitoric systems to more general systems (including those with so-called hyperbolic points, which are more common in nature) (3) explore the connection between semitoric systems, integrable systems, and Floer theory.

Keywords:INTEGRABLE SYSTEMS

Disciplines:Dynamical systems and ergodic theory, Mechanics of particles and systems, Differential geometry, General topology