# GDMSeminar: Abstracts of the Talks (2021/9)

**Alain Chenciner **(Observatoire de Paris)

*ABC*

Tuesday, May 11, 2021 , 15:15 GMT

**Abstract**: A as forces, B as shape, C as angular momentum. In this ABC I’ll consider n-body relative equilibria in dimensions greater than 3. The family of n-body configurations which, when submitted to Newtonian or similar attraction, admit a relative equilibrium motion (the “balanced” configurations) then becomes much richer. Also, a given balanced configuration admits a variety of relative equilibria, namely one for each choice of a hermitian structure on the space where the motion really takes place; in general, if the configuration is not central, such relative equilibria are quasi-periodic.

I shall discuss several problems, like the one of deciding what is the smallest dimension in which a given configuration admits a relative equilibrium motion, or when bifurcations from the periodic relative equilibrium of a central configuration may bifurcate into a family of quasi-periodic relative equilibria of balanced configurations.