By Ovidiu Costin, Frédéric Fauvet, Frédéric Menous, David Sauzin
Those are the lawsuits of a one-week foreign convention based on asymptotic research and its purposes. They include significant contributions facing - mathematical physics: PT symmetry, perturbative quantum box thought, 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 relatives of resurgent services with regards to knot conception.
Read or Download Asymptotics in Dynamics, Geometry and PDEs; Generalized Borel Summation, Vol. I PDF
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Extra resources for Asymptotics in Dynamics, Geometry and PDEs; Generalized Borel Summation, Vol. I
Immink) hit independently on the same method – which must also have occurred, time and again, more or less explicitly, to many an analyst grappling with singularities. 11 While there are only two outer generators (which may coalesce into one), there can be any number of inner generators. 12 Which is only natural, since the outer generators can be interpreted as inÀnite sums of (selfreproducing) inner generators. 43 Power series with sum-product Taylor coefﬁcients and their resurgence algebra So much for the local aspect.
3 The ingress factor . . . . . . . . . . . 1 Bernoulli numbers and polynomials . . . . 2 Resurgence of the Gamma function . . . . 3 Monomial/binomial/exponential factors . . . 4 Resummability of the total ingress factor . . 5 Parity relations . . . . . . . . . 4 Inner generators . . . . . . . . . . . 1 Some heuristics . . . . . . . . . 2 The long chain behind nir//mir . . . . . 3 The nir transform . . . . . . . . . 4 The reciprocation transform .
Apart from their applications to analytic knot theory and the so-called “Volume Conjecture”, SP-series are interesting in their own right, on at least four counts: (i) they generate quite distinctive resurgence algebras (ii) they are one of those relatively rare instances when the resurgence properties have to be derived directly from the Taylor coefÀcients (iii) some of them produce singularities that unexpectedly verify Ànite-order differential equations (iv) all of them are best handled with the help of two remarkable, inÀnite-order integral-differential transforms, mir and nir.