18.385J | Fall 2014 | Graduate

Nonlinear Dynamics and Chaos


In addition to the topics below, we may have time for other topics, such as: Floquet Theory, Infinite Dimensional Hamiltonians, On-Off Dissipative Systems, etc.

1 One-dimensional Systems and Elementary Bifurcations (about two weeks)
2 Two-dimensional Systems; Phase Plane Analysis, Limit Cycles, Poincaré-Bendixson Theory (about two weeks)
3 Nonlinear Oscillators, Qualitative and Approximate Asymptotic Techniques, Hopf Bifurcations (about two weeks)
4 Lorenz and Rossler Equations, Chaos, Strange Attractors and Fractals (about 2.5 weeks)
5 Iterated Mappings, Period-doubling, Chaos, Renormalization, Universality (about 1.5 weeks)
6 Hamiltonian Systems; Complete Integrability and Ergodicity (about 1.5 weeks)
7 Area Preserving Mappings, KAM Theory (about 1.5 weeks)

Course Info

As Taught In
Fall 2014
Learning Resource Types
Problem Sets
Lecture Notes