Vanishing Twist near Focus-Focus Points

Details Vanishing Twist near Focus-Focus Points Vanishing Twist near Focus-Focus Points

2003-06-27

arxiv.org/abs/math/0306392v1

Nonlinearity, 17:1777--1786, 2004

Mathematics

Dynamical Systems

13 pages

Scientific paper

10.1088/0951-7715/17/5/012

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.

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