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.
