Geometry & Topology Seminar: "Symplectic Integrators and Dissipatively Perturbed Hamiltonian Systems"

Abstract: Since Hamiltonian systems have symplectic flows, it is often advantageous to use symplectic integrators when solutions must be approximated numerically. Interestingly, the advantages of these methods persist for dissipatively perturbed Hamiltonian systems, even though such systems no longer have symplectic flows. This talk will give an overview of the underlying theory, as well as presenting some novel numerical methods, whose applications include the Van der Pol oscillator and the Hodgkin-Huxley equations of neuronal dynamics.

Host: Xiang Tang