Introduction to the dynamics of area--preserving maps

Confinement of charged particles in electromagnetic fields, plasma heating, intermolecular dynamics, etc. can all be modeled by Hamiltonian systems dq/dt = partialH(q,p,t)/partialp dp/dt = -partialH(q,p,t)/partialq where q and p are n-dimensional, H is the Hamiltonian, n the number of degrees of freedom, and (p,q) is the phase space. These lectures are structured to describe such Hamiltonian systems in the simplest non-trivial case, i.e., two degree of freedom. In this case the systems can be reduced to iteration of one- parameter families of area-preserving maps of a surface to itself: (q/sub n//sub +/1,p/sub n//sub +/1) = F(q/sub n/,p/sub n/). Periodic orbits, invariant circles, and cantori are mappings which focus this discussion