Symplectic Twist Maps: Global Variational Techniques (Advanced Series in Nonlinear Dynamics)

This book concentrates mainly on the theorem of existence of periodic orbits for higher dimensional analogs of twist maps. The setting is that of a discrete variational calculus and the techniques involve Conley-Zehnder-Morse theory. They give rise to the concept of ghost tori which are of interest in the dimension 2 case (ghost circles). The debate is oriented somewhat toward the open problem of finding orbits of all (in particular, irrational) rotation vectors.