Differential geometry of optimal control problems and Hamiltonian systems
1. Hamiltonian systems and extremals of optimal control problems. |
2. Jacobi curves associated with trajectories of Hamiltonian systems and with various types of extremals. |
3. Elements of symplectic geometry: Lagrange Grassmannians, Maslov index, Cross-ratio. |
4. Canonical connections and curvatures of Hamiltonian systems and smooth control systems. |
5. Geometry of Jacobi curves: their ranks, weights, derivative curves, curvatures, and fundamental forms. Flat curves. |
6. "Comparizon theorems" for conjugate points. |
7. Application to special classes of systems. |