Sturm’s algorithm and isolating blocks

A topological existence proof for certain solutions of the Newtonian three-body problem is based on the construction of isolating blocks for the flow on an integral manifold. An isolating block is a submanifold whose boundary satisfies a convexity condition with respect to the three-body flow. Verifying this convexity condition can be reduced to the problem of checking the sign of a very complicated function of one variable. This can be done numerically, but the goal of this paper is to show that Sturm’s algorithm can be used to provide rigorous verification in some cases.