U.S.-France Cooperative Research: Qualitative Properties inDynamics and Mathematical Physics

这个为期三年的奖项支持美国-法国合作研究 在应用数学中。 该提案涉及两项研究 由格鲁吉亚的杰克黑尔领导的美国和法国的组织 技术研究所和大学的Genevieve Raugel 巴黎南部（奥赛）。 研究人员建议研究 无限维动力学的定性性质，物理的 系统. 这种系统通常由部分 微分方程（PDE）或无穷常微分方程组 微分方程（ODE）或通过一些无限的映射 维数集 利用这些方法和其他有关 数学物理和量子系统，研究人员将 研究了一些具体问题：（1）流的性质 如耗散PDE所定义;（2）湍流（空间- 时间混沌），相干结构，并在扩展 动力系统;（3）性质之间的关系 扩散的相空间和光谱之间的 薛定谔算子与动力系统的排斥子。 格鲁吉亚技术小组研究动力学问题 系统通过研究常微分方程和 地图他们为这种合作带来了功能方面的专业知识， 分析和数学物理。 奥赛小组由 偏微分方程应用于 在动力系统中。 他们精通算子理论 C*-代数 他们的共同努力将扩展理论 从动力系统到偏微分方程。

This three-year award supports U.S.-France cooperative research in applied mathematics. The proposal involves two research groups in the U.S. and France led by Jack Hale of the Georgia Institute of Technology and Genevieve Raugel of the University of Paris, South (Orsay). The investigators propose to study the qualitative properties of infinite dimensional dynamical, physical systems. Such systems are usually described by partial differential equations (PDE) or by infinite systems of ordinary differential equations (ODE) or by maps of some infinite dimensional sets. Utilizing these methods and others related to mathematical physics and quantum systems, the investigators will investigate some concrete problems: (1) the properties of flows as defined by dissipative PDE; (2) notions of turbulence (space- time chaos), coherent structures, and intermittency in extended dynamical systems; and (3) relationships between the properties of diffusion in phase space and between the spectrum of the Schrodinger operator and repellers of dynamical systems. The Georgia Tech group approaches problems of dynamical systems through the study of ordinary differential equations and maps. They bring to this collaboration expertise in functional analysis and mathematical physics. The Orsay group consists of specialists in partial differential equations as applied to problems in dynamical systems. They are well versed in operator theory and C*-algebras. Their combined efforts will extend the theory of dynamical systems to partial differential equations.