The affine invariant of proper semitoric integrable systems

Wednesday, 11 October, 2017

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Nonlinearity, Volume 30, Number 11

This paper initiates the study of semitoric integrable systems with two degrees of freedom and with proper momentum-energy map, but with possibly nonproper S 1-momentum map. This class of systems includes many standard examples, such as the spherical pendulum. To each such system we associate a subset of [$ \newcommand{\R}{{{\mathbb R}}} \R^2$] , invariant under a natural notion of isomorphism and encoding the integral affine structure of the singular Lagrangian fibration, in the spirit of Delzant polygons for toric systems.


Álvaro Pelayo
Tudor S Ratiu
San Vu Ngọc