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Research
Dynamical Systems & Ordinary Differential Equations
Dynamical systems is the study of processes that evolve in time; it includes "chaos theory," Newtonian mechanics, and the modern theory of ordinary differential equations (ODEs). The Mathematical Sciences Department at UC has a long history of excellence in dynamical systems, particularly in the areas of celestial mechanics and bifurcation theory. Present areas of research include: celestial mechanics, smooth foliations, bifurcations, averaging methods for ODEs, Hamiltonian mechanics, fixed point theory, applications of ODE techniques to PDEs and vice-versa, and global invariants and integrability of ODEs.
UC's dynamics group is also involved in a number of collaborative projects in other disciplines and with researchers at other institutions. These range from problems of control and optimization (UC College of Engineering and Georgia Tech), to computer-assisted computation (UC College of Engineering and Univ. of Pamplona, Spain), beam stability in particle accelerators (Univ. of New Mexico, Cornell Univ. and DESY-Hamburg), and problems in the kinetic theory of multi-particle systems (Univ. of Paris).
Faculty
Roger Chalkley, ordinary differential equations
Scott Dumas, dynamical systems, applications to physics
Phil Korman, differential equations
Anthony Leung, singular perturbations
Chris McCord, algegraic topology, dynamical systems
Pat McSwiggen, dynamical systems
Ken Meyer (Taft Professor emeritus), dynamical systems
Dieter Schmidt (Department of Computer Science), celestial mechanics, symbolic computation