The semi-global symplectic invariant is derived for the champagne bottle potential via Birkhoff normal form near the focus-focus point and compared to the spherical pendulum.
Dullin, Semi-global symplectic invariants of the spherical pendulum, J
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Semi-global symplectic invariant of the champagne bottle
The semi-global symplectic invariant is derived for the champagne bottle potential via Birkhoff normal form near the focus-focus point and compared to the spherical pendulum.