B.A. 1966 (Harvard)
Ph.D. 1970 (California at Berkeley)
Guckenheimer came to Cornell in 1985 from the University of California at Santa Cruz, where he had been a member of the faculty since 1973. He has had fellowships or visiting appointments at Instituto Matemática Pura e Aplicada in Rio de Janeiro (1969), University of Warwick (1969-70), Institute for Advanced Study (1970-72, 1988-89), Courant Institute for Mathematical Sciences (1978), Institut des Hautes Études Scientifiques (1979), Mathematical Sciences Research Institute (1983-84), and Institut Mittag-Leffler (1984). He was a Guggenheim fellow in 1984, and was elected president of the Society for Industrial and Applied Mathematics in 1996.
The focus of my studies is dynamical systems. Dynamical systems theory describes general phenomena that occur over long times in deterministic systems. Much of my theoretical work involves study of the iterations of a single, real-valued function and the influence of symmetry on generic features of dynamical systems. Recent research focuses upon methods for computing aspects of dynamical behavior. The computational emphasis has been on computing bifurcations in systems that depend upon parameters and upon producing computer-generated proofs for qualitative properties of phase portraits. I have also studied the application of dynamical systems theory to many fields of science and engineering. I have worked with applications in biology, chemistry, engineering, and physics. Current work focuses on applications to the neurosciences to problems of control. I am collaborating with Ronald Harris-Warrick (Section of Neurobiology and Behavior) in studies of pattern generation in a small neural network, the stomatogastric ganglion of crustacea.
