A Nonlinear Quasiperiodic Mathieu Equation

Monday, October 29, 2001 - 2:00pm - 3:00pm
Keller 3-180
Richard Rand (Cornell University)
This talk presents some recent results obtained regarding the differential equation x + (d + e cos t + e cos wt) x + a x3 = 0. Stability of the origin is investigated using Lyapunov exponents, regular and singular perturbations, and harmonic balance. Computer algebra is utilized to handle the complicated resulting algebraic expressions. In addition, large amplitude subharmonic motions are investigated by using Lie transforms with elliptic functions. The resulting approximations are used to predict the transition from local to global chaos by the use of Chirikov's overlap criterion. This work is joint with Randy Zounes, Stephanie Mason and Rachel Hastings.