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Analytic invariants for the 1 : - 1 resonance

José Pedro Gaivão (2013)

Annales de l’institut Fourier

Associated to analytic Hamiltonian vector fields in 4 having an equilibrium point satisfying a non semisimple 1 : - 1 resonance, we construct two constants that are invariant with respect to local analytic symplectic changes of coordinates. These invariants vanish when the Hamiltonian is integrable. We also prove that one of these invariants does not vanish on an open and dense set.

Asymptotic analysis and special values of generalised multiple zeta functions

M. Zakrzewski (2012)

Banach Center Publications

This is an expository article, based on the talk with the same title, given at the 2011 FASDE II Conference in Będlewo, Poland. In the introduction we define Multiple Zeta Values and certain historical remarks are given. Then we present several results on Multiple Zeta Values and, in particular, we introduce certain meromorphic differential equations associated to their generating function. Finally, we make some conclusive remarks on generalisations of Multiple Zeta Values as well as the meromorphic...

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