2003/06/27 by Holger R. Dullin, Vu Ngoc San
Mathematics · Physics and Astronomy · #math.DS #math.SG #nlin.SI #msc:37J35 #msc:37J15 #msc:37J40 #msc:70H06 #msc:70H08 #msc:37G20
paper · pdf · doi:10.1088/0951-7715/17/5/012
published as Nonlinearity, 17:1777--1786, 2004 · 13 pages
arxiv created 2003/06/27 · arxiv updated 2009/11/30
We show that near a focus-focus point in a Liouville integrable Hamiltonian system with two degrees of freedom lines of locally constant rotation number in the image of the energy-momentum map are spirals determined by the eigenvalue of the equilibrium. From this representation of the rotation number we derive that the twist condition for the isoenergetic KAM condition vanishes on a curve in the image of the energy-momentum map that is transversal to the line of constant energy. In contrast to this we also show that the frequency map is non-degenerate for every point in a neighborhood of a focus-focus point.