Journal of Geometry and Symmetry in Physics

The Adiabatic Limit for Multidimentsional Hamiltonian Systems

Maurice A. de Gosson

Full-text: Open access

Abstract

We study some properties of multidimensional Hamiltonian systems in the adiabatic limit. Using the properties of the Poincare-Cartan invariant we show that in the integrable case conservation of action requires conditions on the frequencies together with conservation of the product of energy and period. In the ergodic case the most general conserved quantity is not volume but rather symplectic capacity; we prove that even in this case there are periodic orbits whose actions are conserved.

Article information

Source
J. Geom. Symmetry Phys., Volume 4 (2005), 19-43.

Dates
First available in Project Euclid: 20 May 2017

Permanent link to this document
https://projecteuclid.org/euclid.jgsp/1495245721

Digital Object Identifier
doi:10.7546/jgsp-4-2005-19-43

Mathematical Reviews number (MathSciNet)
MR2211575

Zentralblatt MATH identifier
1132.37318

Citation

de Gosson, Maurice A. The Adiabatic Limit for Multidimentsional Hamiltonian Systems. J. Geom. Symmetry Phys. 4 (2005), 19--43. doi:10.7546/jgsp-4-2005-19-43. https://projecteuclid.org/euclid.jgsp/1495245721


Export citation