EN FR
EN FR


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 obvious applications in optimal control to compute the global optimum; it is also relevent in optimal transport where regularity properties of the transport map in the Monge problem is related to convexity properties of the tangent injectivity domains.

In [3] , we complete the previous results obtained in [27] (we bring them from ellipsoids to general revolutions surfaces).

The conjugate and cut loci in Serret-Andoyer metrics and dynamics of spin particles with Ising coupling are analized in [7] , this is a first step towards the computation of conjugate and cut loci on left invariant Riemannian and sub Riemannian metrics in S0(3) with applications for instance to the attitude control problem of a spacecraft.

An analysis of singular metrics on revolution surfaces, motivated by the average orbital transfer problem when the thrust direction is restricted, is proposed in [2] .

Finally, [8] determines cut and conjugate loci in an enegy minimizing problem that is related to the quantum systems mentionned in the first paragraph of section 4.2 .