Monotone twist mappings and the calculus of variations
- 1 June 1986
- journal article
- research article
- Published by Cambridge University Press (CUP) in Ergodic Theory and Dynamical Systems
- Vol. 6 (3) , 401-413
- https://doi.org/10.1017/s0143385700003588
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 ℝ × 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: where F has period 1 in t and x and satisfies the Legendre condition Fẋẋ>0.Keywords
This publication has 2 references indexed in Scilit:
- Some remarks on Birkhoff and Mather twist map theoremsErgodic Theory and Dynamical Systems, 1982
- Existence of quasi-periodic orbits for twist homeomorphisms of the annulusTopology, 1982