Аннотация:
For a generic minimum time problem on the plane, we study the projections
of the support of extremals (regarded as a two-dimensional object, after
normalization) from $\mathbb R^2\times S^1$ to $\mathbb R^2$. Moreover, we
study the topology of the reachable set and we give a positive answer to a question of V. I. Arnold: Is the minimum time function, generically, a Morse
function in topological sense?