Vladimir Zakalyukin

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.