Nilpotent orbits and codimension-two defects of 6d N=(2,0) theories

We study the local properties of a class of codimension-2 defects of the 6d N=(2,0) theories of type J=A,D,E labeled by nilpotent orbits of a Lie algebra \mathfrak{g}, where \mathfrak{g} is determined by J and the outer-automorphism twist around the defect. This class is a natural generalisation of the defects of the 6d theory of type SU(N) labeled by a Young diagram with N boxes. For any of these defects, we determine its contribution to the dimension of the Higgs branch, to the Coulomb branch operators and their scaling dimensions, to the 4d central charges a and c, and to the flavour central charge k.Comment: 57 pages, LaTeX2

On the co-existence of maximal and whiskered tori in the planetary three-body problem

none1noIn this paper we discuss about the possibility of {it coexistence} of stable and unstable quasi--periodic {sc kam} tori in a region of phase space of the three-body problem. The {argument of proof} goes along {{sc kam} theory and, especially,} the production of two non smoothly related systems of canonical coordinates in the same region of the phase space, the possibility of which is foreseen, for ``properly--degenerate' systems, by a theorem of Nekhorossev and Mi{{s}}{{c}}enko and Fomenko. The two coordinate systems are alternative to the classical reduction of the nodes by Jacobi, described, e.g., in~Ref.cite[III,S 5, n. 4, p. 141]{arnold63}.mixedGabriella PinzariPinzari, Gabriell