Stable Morse Decompositions for Piecewise Constant Vector Fields on Surfaces: Supplementary Material

Admissibility is a technical condition that ensures that the fixed point index of the flow is well-defined [Gor06]. Recall that a flow is admissible if and only if it is upper semicontinuous (i.e. if the limit of a convergent sequence of trajectories is a trajectory) and if there exists h > 0 such that, for any point x, the set of trajectory segments S(x,h) starting at x and defined on the time interval [0,h] is contractible.