By Christian Bogner, Stefan Weinzierl (auth.), Ovidiu Costin, Frédéric Fauvet, Frédéric Menous, David Sauzin (eds.)
These are the lawsuits of a one-week foreign convention established on asymptotic research and its purposes. They include significant contributions facing: mathematical physics: PT symmetry, perturbative quantum box concept, WKB research, neighborhood dynamics: parabolic structures, small denominator questions, new elements in mold calculus, with similar combinatorial Hopf algebras and alertness to multizeta values, a brand new relations of resurgent features relating to knot theory.
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Extra info for Asymptotics in Dynamics, Geometry and PDEs; Generalized Borel Summation vol. II
7 Dimorphic isomorphisms in polar mode . . . Singulators, singulands, singulates . . . . . . 1 Some heuristics. 2 Universal singulators senk(ess• ) and seng(es• ) . 3 Properties of the universal singulators . . . 4 Polar singulators: description and properties . . 5 Simple polar singulators . . . . . . . 6 Composite polar singulators . . . . . . 7 From al/al to al/il. Nature of the singularities . A natural basis for ALIL ⊂ ARI al/il . . . . . . 1 Singulation-desingulation: the general scheme .
The total effect is thus a drastic and welcome ‘division by twelve’ of the flexion jungle. Throughout, there is as much emphasis on the apparatus – the flexion structure and its special bimoulds – as on the applications to multizeta theory. We wind up with a sketch of perinomal algebra, in the hope of stimulating interest in this brand-new subject and of paving the way for a collective programme of exploration,21 to start hopefully in the course of 2011. One last word of caution: throughout this paper, the somewhat contentious word canonical is never used as a substitute for unique (when meaning unique, we say unique) but as a pointer to the existence, within a class of seemingly undistinguishable objects (like the many conceivable systems of multizeta irreducibles) of genuinely privileged representatives.
A• ), B • ). 48) assopreari(A• , B • , C • ) ≡ assopreari(A• , C • , B • ) with assopreari denoting the associator27 of the pre-bracket preari. The same holds of course for ami and ani. e. from left to right: preari(A•1 , . . , A•s ) = preari(preari(A•1 , . . 49) we have a simple expression for the exponential mapping from a Lie algebra to its group. Thus, the exponential expari : ARI → GARI can be expressed as a series of pre-brackets: n times expari(A• ) = 0≤n 1 1 preari( A• , . . , A• ) = 1•+ preari(.