In honor of the 100th birthday of the article, " Sur les groupes continus " Abstract: A methodical analysis of the research related to the article , " Sur les groupes continus " , of Henri Poincaré reveals many historical misconceptions and inaccuracies regarding his contribution to Lie theory. A thorough reading of this article confirms the precedence of his discovery of many important concept...

The n Birkhoff polytope is the set of all doubly stochastic n × n matrices, that is, those matrices with nonnegative real coefficients in which every row and column sums to one. A wide open problem concerns the volumes of these polytopes, which have been known for n ≤ 8. We present a new, complex-analytic way to compute the Ehrhart polynomial of the Birkhoff polytope, that is, the function coun...

We prove that a Hamiltonian p ∈ C(T R) is locally integrable near a nondegenerate critical point ρ0 of the energy, provided that the fundamental matrix at ρ0 has no purely imaginary eigenvalues. This is done by using Birkhoff normal forms, which turn out to be convergent in the C sense. We also give versions of the Lewis-Sternberg normal form near a hyperbolic fixed point of a canonical transfo...

We formulate a general institution-independent (i.e. independent of the details of the actual logic formalised as institution) version of the Craig Interpolation Theorem and prove it in dependence of Birkhoff-style axiomatizability properties of the actual logic. We formalise Birkhoff-style axiomatizability within the general abstract model theoretic framework of institution theory by the novel...

The purpose of this note is to apply the recent results on semi-classical trace formulæ [17], and on quantum Birkhoff normal forms for semi-classical Fourier Operators [12] to inverse problems. We show how the classical Birkhoff normal form can be recovered from semi-classical spectral invariants. In fact the full quantum Birkhoff normal form of the quantum Hamiltonian near a closed orbit, and ...