Advanced Nonlinear Dynamics and Chaos (18.386J/2.037J)
George Haller (2x3064, Rm. 3-352, ghaller at mit dot edu)
|Office hours:||Tuesday, 2:00-3:00pm
Introductory slides (PDF)
This graduate course discusses advanced topics from the modern theory of nonlinear dynamical systems. Applications will primarily be selected from mechanics and fluid dynamics. Prerequisites: 18.385J/2.036J or equivalent.
Crash course on manifolds; existence, persistence, and smoothness; geometric singular perturbation theory
Homoclinic bifurcations; higher-dimensional Melnikov methods; Shilnikov orbits
The internal structrure of chaos
Symbolic dynamics, Bernoulli shift map, subshifts of finite type, higher-dimensional chaos
Canonical and noncanonical Hamiltonians, symplectic geometry, conservation properties, phase space geometry
KAM theory, existence and persistence of invariant tori
Attractors, inertial manifolds; Hamiltonian and dissipative examples
The course will draw topics and applications from several sources, including the following textbooks:
Guckenheimer, J., and Holmes, P., Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
Arnold, V. I., Mathematical Methods of Classical Mechanics
Chicone, C., Ordinary Differential Equations with Applications
These books will be on reserve in Baker Library. There is no required textbook.
Grading: Based on homework.