University： Massachusetts Institute of Technology
Instructors: Prof. Rodolfo R. Rosales
Course Number: 18.385J
This graduate level course focuses on nonlinear dynamics with applications. It takes an intuitive approach with emphasis on geometric thinking, computational and analytical methods and makes extensive use of demonstration software.
In addition to the topics below, we may have time for other topics, such as: Infinite Dimensional Hamiltonian Systems, On-Off Dissipative Systems, etc.
Calendar TOPIC # Topics 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)
Each exam is worth 40% of the grade