MERCREDI 06 OCTOBRE 2010
14 heures
Salle Séminaire 5
Centre de Physique Théorique
Marseille-Luminy

Robert L. Dewar
Research School of Physics and Engineering
The Australian National University
Canberra
ACT 0200 Australia
Coauthors: Ashley M. Gibson

Title: Relation of almost-invariant-torus formulations for area-preserving
maps and 1[1/2] degree-of-freedom continuous-time Hamiltonian systems

Abstract: By using a general formulation in terms of action gradient, the
quadratic-flux-minimizing circles introduced by Meiss and Dewar, and
the ghost circles introduced by Angenent and GolŽ, [1] for
discrete-time symplectic map dynamical systems are shown to be
PoincarŽ sections of almost-invariant tori incontinuous-time
Hamiltonian systems of the kicked-rotor type. As the magnetic field in
a toroidal plasma containment device can be described as a 1[1/2]
degree-of-freedom Hamiltonian dynamical system, this allows
area-preserving maps to be used as "toy models" for exploring new
methods [2] of characterising the dynamics of non-integrable magnetic
field systems.

[1] R.L. Dewar and A.B. Khorev, Rational quadratic-flux minimizing
circles for area-preserving twist maps, Physica D 85, 66-78 (1995)

[2] R.L. Dewar and S.R. Hudson and A.M. Gibson, Unified Theory of
Ghost and Quadratic-Flux-Minimizing Surfaces, accepted for publication
in J. Plasma Fusion Research SERIES 9, 487-490 (2010),
http://www.jspf.or.jp/JPFRS/index_vol9-4.html