August
13 – Discussion and Examples.
16 – Persistence of Fixed Points
20 – Proof of Center Stable/Unstable Manifolds
23 – Proof of Center Stable/Unstable Manifolds
27 – Proof of Center Stable/Unstable Manifolds
30 – No lessons
September
Homework Projects
– Invariant Foliations
– Smoothness of centre manifolds
– Normal forms – Auto package
October
08 – 1d centre manifolds – baby normal forms
11 – 1d centre manifolds – one parameter family
15 – 2d centre manifolds: Hopf Bifurcation 1
22 – 2d centre manifolds: Hopf Bifurcation 2
25 – 2d centre manifolds: SNIC
29 – 2d centre manifolds: Homoclinic
November
05 – Homoclinic bifurcation: Shilnikov
08 – Homoclinic bifurcation: Shilnikov
12 – Homoclinic bifurcation: Shilnikov
15 – Coupled Systems with Periodic Motion: Floquet Theory
19 – Coupled Systems with Periodic Motion: Poincare Map
22 – Coupled Systems with Periodic Motion: Phase response
26 – Coupled Systems with Periodic Motion: Averaging Theory
29 – Kuramoto Model