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In this contribution to the volume in memoriam of Michel Henon, we thought appropriate to look at his early scientific work devoted to the dynamics of large assemblies of interacting masses. He predicted in his PhD thesis that, in such a system, first a collapse of mass occurs at the center and that later binaries stars are formed there. Henceforth, the negative energy of binding of pairs becomes a source of positive energy for the rest of the cluster which evaporate because of that. We examine under what conditions such a singularity can occur, and what could happen afterwards. We hope to show that this fascinating problem of evolution of self-gravitating clusters keeps its interest after the many years passed since Henon thesis, and is still worth discussing now.
Several variants of the classic Fibonacci inflation tiling are considered in an illustrative fashion, in one and in two dimensions, with an eye on changes or robustness of diffraction and dynamical spectra. In one dimension, we consider extension mec
Paper in honour of Michel Henon, based on a talk presented at Institut Henri Poincare, Paris, 5 Decembre 2013.
Grothendieck and Harder proved that every principal bundle over the projective line with split reductive structure group (and trivial over the generic point) can be reduced to a maximal torus. Furthermore, this reduction is unique modulo automorphism
The long timescale evolution of a self-gravitating system is generically driven by two-body encounters. In many cases, the motion of the particles is primarily governed by the mean field potential. When this potential is integrable, particles move on
In this note, we unify and extend various concepts in the area of $G$-complete reducibility, where $G$ is a reductive algebraic group. By results of Serre and Bate--Martin--R{o}hrle, the usual notion of $G$-complete reducibility can be re-framed as a