This course covers the learning outcomes and goals of understanding center manifolds for Hamiltonian systems and PDEs. Students will learn about center manifold bifurcation analysis, inclusion of unstable directions, symplectic Jordan canonical form, and center manifold theory for PDEs. The course also explores a pitchfork bifurcation in a PDE and center manifolds for stochastic systems. The teaching method involves lectures and examples. The intended audience for this course includes students and professionals interested in dynamical systems, bifurcations, and nonlinear dynamics.
Center Manifolds for Hamiltonian Systems and PDEs - Lorenz System Bifurcation, Part 2
Overview
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.
Taught by
Ross Dynamics Lab
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