8 citations · 17 across the 9 of their papers we have counts for
9 papers
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…
Vu Ngoc's Conjecture on focus-focus singular fibers with multiple pinched points
Álvaro Pelayo, Xiudi Tang
We classify, up to fiberwise symplectomorphisms, a saturated neighborhood of a singular fiber of an integrable system (which is proper onto its image and has connected fibers) cont…
Symplectic stability on manifolds with cylindrical ends
Sean Curry, Álvaro Pelayo, Xiudi Tang
A famous result of Jurgen Moser states that a symplectic form on a compact manifold cannot be deformed within its cohomology class to an inequivalent symplectic form. It is well kn…
Moser stability for volume forms on noncompact fiber bundles
Álvaro Pelayo, Xiudi Tang
We prove a stability result for volume forms on fiber bundles with compact base and noncompact fibers. This generalizes the classical results of Moser and Greene--Shiohama, and rec…