Section: New Results

Conjugate and cut loci computations and applications

Participants : Bernard Bonnard, Olivier Cots, Jean-Baptiste Caillau.

One of the most important results obtained by B. Bonnard and his collaborators concern the explicit computations of conjugate and cut loci on surfaces. This has applications in optimal control to compute the global optimum and in optimal transport where regularity properties of the map in the Monge problem is related to convexity properties of the tangent injectivity domains. This shows also the transverse part of the team: [3] complete the previous results obtained with Rifford [33] ; the paper [20] analyses the conjugate and cut loci in Serret-Andoyer metrics and dynamics of spin particles with Ising coupling, and is a first step towards the computation of conjugate and cut loci on left invariant Riemannian and SR- metrics in S0(3) with applications for instance to the attitude control problem of a spacecraft. The submitted paper [19] concerns the analysis of singular metrics on surfaces in relation with the average orbital transfer problem.