Standard syllabus
Dynamical systems · Graduate · Math
Topics
Flows and invariant sets
- Existence and uniqueness for ODEs; maximal intervals of solutions
- Flows, orbits, and invariant sets
- Limit sets, ω-limit sets, and attractors
- Lyapunov stability and Lyapunov functions
- Stable and unstable manifolds (local theory)
Bifurcation theory
- Parameter-dependent equilibria; structural stability (introduction)
- Saddle-node, transcritical, and pitchfork bifurcations
- Hopf bifurcation and limit cycle creation
- Normal forms and center manifold reduction (introduction)
- Codimension-two bifurcations (overview)
Discrete and symbolic dynamics
- Diffeomorphisms and return maps
- Smale horseshoe and symbolic dynamics
- Topological entropy (introduction)
- Period doubling cascade and universality
- Hamiltonian dynamics and KAM theory (overview)
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