MATH 6270 - [Applied Dynamical Systems]

(crosslisted) MAE 7760

Spring. Not offered: 2021-2022. Next offered: 2022-2023. 4 credits. Student option grading.

Prerequisite: MAE 6750, MATH 6260, or equivalent.

Staff.

Topics include review of planar (single-degree-of-freedom) systems; local and global analysis; structural stability and bifurcations in planar systems; center manifolds and normal forms; the averaging theorem and perturbation methods; Melnikov’s method; discrete dynamical systems, maps and difference equations, homoclinic and heteroclinic motions, the Smale Horseshoe and other complex invariant sets; global bifurcations, strange attractors, and chaos in free and forced oscillator equations; and applications to problems in solid and fluid mechanics.