Lagrangian and Legendre singularities in control systems
1. Symplectic and contact geometry of control systems. Lagrangian and Legendre varieties. Caustics and wavefronts. |
2. Generating families of lagrangian and Legendre varieties. Local and global settings. |
3. Arnold theory of simple singularities of wavefronts and caustics. |
4. Generic one-parameter bifurcations of wavefronts. |
5. Nye-Chekanov theorem of admissible bifurcations in pseudooptical case. Maslov class. |
6. Boundary singularities and control theory. |
7. Avoiding an obstacle problem and first examples of stable singular lagrangian varieties. |
Applications to control systems: |
8. Singularites of relative minima function. |
9. Caustic of exponential mapping in contact 3-dimensional subriemannian problem. |
10. Singularities of attainability domains of systems determined by translation invariant finsler metric. |