Advanced Nonlinear Dynamics

Catalog description

The course covers advanced topics in chaos and nonlinear dynamics including center manifolds, homoclinic and heteroclinic tangles and chaotic transport, topology of chaos-branched manifolds, invariant sets, and universality. Also, the symmetry of chaos, chaos in Hamiltonian and conservative systems, KAM theorem, stochastic layers and diffusion, and chaos in quantum systems. Theory will be applied to various systems in physics, chemistry, biology, and other fields. Numerical and computational techniques will be presented and used in the applications.