9 papers · 1 filter
Action-angle coordinates of spherical pendulums with symmetric quadratic potentials
Chengle Peng, Xiudi Tang
We study the spherical pendulum system with an arbitrary potential function , which is an integrable system with a first integral whose Hamiltonian flow is periodic. We…
A note on the symplectic classification of almost-toric systems
Xiudi Tang
Since simple semitoric systems were classified about fifteen years ago, and semitoric systems five years ago, we want to move a step forward to almost-toric systems. We give a clas…
Classifying affine structures with focus-focus singularities
Xiudi Tang
We study the singular affine structures of integrable systems with focus-focus singular fibers on the image of momentum maps. The classification of singular affine structures is eq…
Symplectic excision
Yael Karshon, Xiudi Tang
We use time-independent incomplete Hamiltonian flows to excise interesting closed subsets of positive codimension from symplectic manifolds. Examples of such subsets include what w…
Semitoric systems of non-simple type
Joseph Palmer, Álvaro Pelayo, Xiudi Tang
Within integrable systems, the class of so called "semitoric" integrable systems in dimension four has attracted a lot of attention in recent years, especially since fundamental ex…
Removing a ray from a noncompact symplectic manifold
Xiudi Tang
We prove that any noncompact symplectic manifold which admits a properly embedded ray with a wide neighborhood is symplectomorphic to the complement of the ray by constructing an e…