Local and global problems of singularity theory,
differential equations, optimal control theory, Lagrangian varieties, caustics.
Main publications:
V. M. Zakalyukin, “Lagrangian and Legendrian singularities”, Funct. Anal. Appl., 10:1 (1976), 23–31
V. M. Zakalyukin, “Reconstructions of fronts and caustics depending on a parameter, and versality of mappings”, Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat., 22, 1983, 56–93
V. M. Zakalyukin, “Singularities of Circle-Surface Contacts and Flags”, Funct. Anal. Appl., 31:2 (1997), 131–133
V. V. Goryunov, V. M. Zakalyukin, “Simple symmetric matrix singularities and the subgroups of Weyl groups $A_\mu$, $D_\mu$, $E_\mu$”, Mosc. Math. J., 3:2 (2003), 507–530
J.-P. Gauthier, V. M. Zakalyukin, “On the motion planning problem, complexity, entropy, and nonholonomic interpolation”, J. Dyn. Control Syst., 12:3 (2006), 371–404
