Math 412: Syllabus
Flow in 1D : - fixed points and stability
- phase portraits
- bifurcations
- simple oscillators
Flow in 2D : Linear systems
- eigenvalues,eigenvectors and solutions
- phase portraits
- stability
- bifurcations
Nonlinear systems
- Linearization about fixed points
- nolinear phase portraits
- Limit cycles, Poincare-Bendixson Theorem
- bifurcations
Flow in 3D: Chaos
-Lorenz equations, the Lorenz attractor
-discrete maps: tent map, logistic map
-fractals: dimension of a set, sample fractals
-strange attractors
Periodic flows in nD : Poincare maps (time permitting)