Differential Geometry

Download Asymptotics in Dynamics, Geometry and PDEs; Generalized by Ovidiu Costin, Frédéric Fauvet, Frédéric Menous, David PDF

By Ovidiu Costin, Frédéric Fauvet, Frédéric Menous, David Sauzin

Those are the court cases of a one-week overseas convention headquartered 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 facets in mold calculus, with similar combinatorial Hopf algebras and alertness to multizeta values, - a brand new kin of resurgent features regarding knot conception.

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Asymptotics in Dynamics, Geometry and PDEs; Generalized Borel Summation, Vol. I

Those are the complaints of a one-week foreign convention situated on asymptotic research and its purposes. They comprise significant contributions facing - mathematical physics: PT symmetry, perturbative quantum box thought, WKB research, - neighborhood dynamics: parabolic platforms, small denominator questions, - new features in mold calculus, with similar combinatorial Hopf algebras and alertness to multizeta values, - a brand new family members of resurgent capabilities relating to knot conception.

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Extra info for Asymptotics in Dynamics, Geometry and PDEs; Generalized Borel Summation, Vol. I

Sample text

3 The four gates to the inner algebra . . . . 2 Some resurgence background . . . . . . . . 1 Resurgent functions and their three models . . 2 Alien derivations as a tool for Riemann surface description . . . . . . . . . . 3 Retrieving the resurgence of a series from the resurgence of its Taylor coefÀcients . . . . 3 The ingress factor . . . . . . . . . . . 1 Bernoulli numbers and polynomials . . . . 2 Resurgence of the Gamma function . . . . 3 Monomial/binomial/exponential factors .

2) ( ∈ {0, 1}). Summation starts at = 0 unless F(0) ∈ {0, ∞}, in which case it starts at = 1. 1 The two driving functions F 1 This choice is to ensure near-invariance under the change F(x) → 1/F(1 − x). 5. 38 Jean Ecalle and Shweta Sharma and f are connected under F ≡ exp(− f ). e. when f is holomorphic. ). As for the above deÀnition, it is less arbitrary than may seem at Àrst sight. Indeed, none of the following changes: (i) changing the grid {k/n} to {Const k/n} (ii) changing the lower summation bounds from 0 or 1 to 2,3 .

2) ( ∈ {0, 1}). Summation starts at = 0 unless F(0) ∈ {0, ∞}, in which case it starts at = 1. 1 The two driving functions F 1 This choice is to ensure near-invariance under the change F(x) → 1/F(1 − x). 5. 38 Jean Ecalle and Shweta Sharma and f are connected under F ≡ exp(− f ). e. when f is holomorphic. ). As for the above deÀnition, it is less arbitrary than may seem at Àrst sight. Indeed, none of the following changes: (i) changing the grid {k/n} to {Const k/n} (ii) changing the lower summation bounds from 0 or 1 to 2,3 .

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