Mathematical Sciences: New Directions in Integrable Systems

可积系统理论的新领域：1)格子可积系统的精确时间离散化和相关的无限精确计数格式；2)离散可积系统的Q-模拟；3)源于量子群的经典力学的扰动；4)可积系统的相对论模拟；5)无限维哈密顿系统和可积系统的几何扰动本方案寻求解决下列公开问题：1)基本连续系统的无误差数值逼近的构造；2)这些量子效应的量子化，以及这些量子效应对经典系统的一阶影响；3)经典重要非相对论系统的相对论版本；4)动力系统的不变性分析(即独立于任何特定的观点)。

New areas in the theory of integrable systems: 1)Exact time-discretizations of lattice integrable systems and related infinitely-precisenumerical schemes; 2)q-analogs of discrete integrable systems; 3)Perturbations of classical mechanics originating in Quantum Groups; 4)Relativistic analogs of integrable systems; 5)Geometric perturbations of infinite-dimensional Hamiltonian and integrable systems The proposal seeks to develop solutions to the following open problems: 1)Construction of error-free numerical approximations to fundamental continuous systems; 2)Quantisations of these, and first-order influence of these quantum effects on classical systems; 3)Relativistic versions of classically important nonrelativistic systems; 4)Invariant analysis (i.e. independent of any particular point of view) of dynamical systems.