Mathematical Sciences: New Directions in Integrable Systems

可积系统理论的新领域：1）精确 格点可积系统的时间离散化及相关 无限精度格式; 2）离散格式的q-模拟 可积系统; 3）经典力学的扰动 起源于量子群; 4）相对论类似物 可积系统; 5）几何扰动 无限维Hamilton系统与可积系统 该提案旨在为以下问题制定解决方案 开放问题：1）无误差数值构造 基本连续系统的近似; 2）量子化 以及这些量子效应对 经典系统; 3）经典的相对论版本 重要的非相对论系统; 4）不变量分析（即 独立于任何特定的观点）的动态的 系统.

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.