Twist Maps and Invariant Curves

Abstract

In this chapter we study the dynamics of area-preserving (i.e., symplectic) monotone twist maps of the annulus. While seemingly quite special, we have already seen examples of such maps as time one maps of time periodic Hamiltonian systems of one degree of freedom, as Poincaré section maps for periodic orbits of Hamiltonian systems of two degrees of freedom (see Chapter V, Sections B and E). These maps also appear as dynamical systems in their own right (e.g., biliards on a convex table and one-dimensional crystals; see V.B).