1. Autonomous Differential Equations of First-order
- Critical points, stability, linear stability analysis, existence and uniqueness, bifurcations
2. Autonomous Systems on the plane
- Linear Systems: classification, stable and unstable manifolds, phase diagrams
- Non-Linear Systems: topological equivalence, critical points and linearization, phase diagrams
- Limit cycles: existence and uniqueness, rule-out limit cycles
- Bifurcations: saddle-node, transcritical, pitchfork, Hopf
- Hamiltonian Systems, Gradient Systems, Reversible Systems
3. Poincare maps and non-autonomous systems on the plane
4. Three-Dimensional Autonomous Systems and Chaos
- Linear and non-linear systems: critical points, stability, phase diagrams
- Lorenz equations: properties, critical points, asymptotic stability, strange tractors, chaos
5. Discrete Dynamic Systems
- Linear and nonlinear discrete systems: fixed points, stability, cobwebs, periodic solutions, trajectories, period doubling sequences
- Triangular map
- Logistic map and the Feigenbaum constant
6. Complexity
- Complex iterations
- Fractals
- Networks
