Monotone twist mappings and the calculus of variations

Abstract

It is shown that a smooth area-preserving monotone twist mapping φ of an annulus A can be interpolated by a flow φt which is generated by a t-dependent Hamiltonian in [formula omitted] × A having the period 1 in t and satisfying a Legendre condition. In other words, any such monotone twist mapping can be viewed as a section mapping for the extremals of variational problem on a torus: [formula omitted] where F has period 1 in t and x and satisfies the Legendre condition Fẋẋ>0. © 1986, Cambridge University Press. All rights reserved.