Morse properties for the minimum time function on 2-D manifolds (Q1868372)

The authors study the problem of steering a point \(p\in M\) of a two-dimensional manifold \(M\) to a point \(q\in M\) in minimum time, using integral curves of two given smooth vector fields \(X\) and \(Y\) on \(M\). Using the notion of the minimum time fronts (level sets of the minimum time function; cf. [\textit{V. I. Arnol'd}, Catastrophe theory 3rd ed. (1992; Zbl 0746.58001), \textit{V. I. Arnol'd}, \textit{S. M. Gusein-Zade} and \textit{A. N. Varchenko}, Singularities of differentiable maps, Monogr. Math. 82 (1985; Zbl 0554.58001) and ibid. 83 (1988; Zbl 0659.58002)]), it is proved that the minimum time function is a Morse function in topological sense.