完全可积系统的正则变形

Poisson surfaces and algebraically completely integrable systems

One can associate to many of the well known algebraically integrable systems of Jacobians (generalized Hitchin systems, Sklyanin) a ruled surface which encodes much of its geometry. If one looks at the classification of such surfaces, there is one case of a ruled surface that does not seem to be covered. This is the case of projective bundle associated to the first jet bundle of a topologically nontrivial line bundle. We give the integrable system corresponding to this surface; it turns out to be a deformation of the Hitchin system.

Optimal transport on completely integrable toric manifolds

We show that existence and uniqueness of solutions to transported Monge-Ampere problem on complex compact toric manifold follows easily from the real theory of optimal transportation.

作为共各向同性形变的无色散可积方程。扩张和缩小

Dispersionless integrable equations as coisotropic deformations. Extensions and reductions

本文讨论了无色散可积族作为某些代数和其它代数结构（如Jordan三系）的共各向同性变形方程的解释。几个概括被认为是。无色散可积方程的定态约化与平面上的动力系统在固定能级上完全可积有关。讨论了EMS。几个概括被认为是。无色散可积方程的定态约化与平面上的动力系统在固定能级上完全可积有关。

半经典完全可积系统的辛技巧

Symplectic Techniques for Semiclassical Completely Integrable Systems

本文从局域"相空间“分析的观点出发，综述了经典和量子完全可积系统。它提倡使用范式，并展示了如何从粘合局部片段中获得全局信息。许多重要的现象，如monodromy或本征值浓度所示，产生的非退化临界点的存在。

Completely integrable torus actions on complex manifolds with fixed points

We show that if a holomorphic $n$ dimensional compact torus action on a compact connected complex manifold of complex dimension $n$ has a fixed point then the manifold is equivariantly biholomorphic to a smooth toric variety.

完全可积系统非退化条件的几何

The geometry of nondegeneracy conditions in completely integrable systems

在K.A.M.定理中需要施加非退化条件，以确保丢番图环面的集合具有大的测度。虽然它们通常用作用量坐标表示，但可以用正则完全可积系统的概念给出一个几何公式，该系统由拉格朗日环面对辛流形的纤维化以及纤维上的哈密顿函数常数定义。本文给出了各种非退化条件的几何定义，给出了它们之间的蕴涵关系，并证明了非退化Hamilton算子纤维化的唯一性。

Symplectic theory of completely integrable Hamiltonian systems

This paper explains the recent developments on the symplectic theory of Hamiltonian completely integrable systems on symplectic 4-manifolds, compact or not. One fundamental ingredient of these developments has been the understanding of singular affine structures. These developments make use of results obtained by many authors in the second half of the twentieth century, notably Arnold, Duistermaat and Eliasson, of which we also give a concise survey. As a motivation, we present a collection of remarkable results proven in the early and mid 1980s in the theory of Hamiltonian Lie group actions b…

拟Frobenius代数及其由常黎曼曲率相容（N × N）-度量生成的可积N-参数变形

Quasi-Frobenius algebras and their integrable N-parametric deformations generated by compatible (N x N)-metrics of constant Riemannian curvature

我们证明了相容的（N × N）-度量束的常数黎曼曲率的描述是等价于一类特殊的可积N-参数变形的拟Frobenius（一般来说，非交换）代数。

关于部分可积哈密顿系统的KAM定理的注记

A note on the KAM theorem for partially integrable Hamiltonian systems

本文给出了部分可积哈密顿系统到完全可积系统的辛约化。KAM定理被应用到这个约化的完全可积的哈密顿系统。它的KAM扰动产生了原来的部分可积系统的扰动，使得由这个扰动保持的环面集是大的。

Completely Integrable Contact Hamiltonian Systems and Toric Contact Structures on $S^2\times S^3$

I begin by giving a general discussion of completely integrable Hamiltonian systems in the setting of contact geometry. We then pass to the particular case of toric contact structures on the manifold $S^2\times S^3$. In particular we give a complete solution to the contact equivalence problem for a class of toric contact structures, $Y^{p,q}$, discovered by physicists by showing that $Y^{p,q}$ and $Y^{p',q'}$ are inequivalent as contact structures if and only if $p\neq p'$.

结合代数的余迷向变形与无色散可积族

Coisotropic deformations of associative algebras and dispersionless integrable hierarchies

本文探讨了无色散可积族理论的代数基础，如无色散KP族和修正KP族以及亏格为零的泛Whitham族。它突出的想法解释这些层次作为方程的各向同性变形的结构常数的某些结合代数。它讨论了结构常数和Hirota的tau函数之间的联系，并表明，在这种方法中，色散Hirota的双线性方程是一种写的结合性条件的结构常数的tau函数。它还提出了一个简单的解释代数几何结构的普遍Whitham方程的亏格为零，由于Krichever。