From semitoric systems to integrable dynamics and Floer theory (Int Sys Floer).

Semitoric systems are a type of dynamical system which satisfy certain symmetries. These systems can be well understood in terms of five invariants. 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). This project will (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 common in nature) (3) explore the connection between semitoric systems, integrable systems, and Floer theory.

Keywords:SYMPLECTIC GEOMETRY, FLOER HOMOLOGY, HAMILTONIAN, DYNAMICAL SYSTEMS

Disciplines:Dynamical systems and ergodic theory, Ordinary differential equations, Differential geometry