Center Manifolds for Hamiltonian Systems and PDEs - Lorenz System Bifurcation, Part 2

Explore advanced concepts in dynamical systems theory through a comprehensive lecture on center manifolds for Hamiltonian systems and PDEs. Delve into the center manifold bifurcation analysis of the Lorenz system, examine the inclusion of unstable directions in Hamiltonian systems, and investigate center manifolds for partial differential equations. Learn about symplectic Jordan canonical form, pitchfork bifurcations in PDEs, and applications to flame front evolution models. Gain insights into the collinear Lagrange points of the planar circular restricted three-body problem and discover how center manifold theory extends to stochastic systems and other computational methods.

Syllabus

center manifold bifurcation analysis for the Lorenz system.
Inclusion of unstable directions.
Example: saddle-center point of a Hamiltonian system.
Symplectic Jordan canonical form.
Center manifold theory for PDEs.
a pitchfork bifurcation in a PDE.
Center manifolds for stochastic systems, and other computational methods.