Arnold's seminar
November 23, 1999

V.Zakalyukin
"On subriemannian caustics for contact distributions in three-space"

Consider a non-integrable istribution on three-space endowed with a
Riemannian metric. In 1995 Agrachev and later Gauthier calculated the locus
of the first conjugate points along the subriemannian geodesics (local
minimisers of length among the admissible curves whose velocities belong to
the distribution) issuing from the origin. This caustic looks "like" D4
pyramid caustic but with four cuspidal edges. The question of its stability
was among the Arnold's seminar problems since 1995. We prove the existence
of moduli and on the other hand prove the stability of the corresponding big
front.