Format:
Online-Ressource (450p, digital)
ISBN:
9788876423796
Series Statement:
Publications of the Scuola Normale Superiore, CRM Series 12
Content:
C. M. Bender, D. W. Hook, K. S. Kooner: Complex Elliptic Pendulum -- F. Bracci: Parabolic attitude -- J. Ecalle, S. Sharma: Power series with sum-product Taylor coefficients and their resurgence algebra -- J. Raissy: Brjuno conditions for linearization in presence of resonance -- J.-Y. Thibon: Noncommutative symmetric functions and combinatorial Hopf algebras -- C. Bogner, S. Weinzierl: Feynman graphs in perturbative quantum field theory -- A. J. Corcho, F. Linares, C. Matheus: Multilinear estimates for the 2D and 3D Zakharov-Rubenchik systems -- J. Ecalle: The flexion structure and dimorphy: flexion units, singulators, generators, and the enumeration of multizeta irreducible -- J. Ecalle: (title to follow) -- S. Kamimoto, T. Kawai, T. Koike, Y. Takei: On a Schrödinger equation with a merging pair of a simple pole and a simple turning point – Alien calculus of WKB solutions through microlocal analysis -- R. Schäfke: (title to follow).
Content:
These are the proceedings of a one-week international conference centered on asymptotic analysis and its applications. They contain major contributions dealing with - mathematical physics: PT symmetry, perturbative quantum field theory, WKB analysis, - local dynamics: parabolic systems, small denominator questions, - new aspects in mould calculus, with related combinatorial Hopf algebras and application to multizeta values, - a new family of resurgent functions related to knot theory.
Note:
Auf Homepage von Springer unter der Reihe „Publications of the Scuola Normale Superiore“ aufgeführt
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Includes bibliographical references
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Title Page; Copyright Page; Table of Contents; Introduction; Authors' affiliations; Complex elliptic pendulum; 1 Introduction; 2 Previous results on complex classical mechanics; 3 Classical particle in a complex elliptic potential; 4 Summary and discussion; References; Parabolic attitude; 1 Introduction; 2 Parabolic dynamics in one variable; 3 Germs tangent to the identity; 4 Semiattractive and quasi-parabolic germs; 4.1 Semiattractive germs; 4.2 Quasi-parabolic germs; 5 One-resonant germs; References; Power series with sum-product Taylor coefficients and their resurgence algebra
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1 Introduction1.1 Power series with coeffcients of sum-product type; The notion of SP series; Special cases of SP series; Overview; 1.2 The outer/inner dichotomy and the ingress factor; The outer/inner dichotomy; A gratifying surprise: the mir-transform; The ingress factor and the cleansing of SP-series; 1.3 The four gates to the inner algebra; 2 Some resurgence background; 2.1 Resurgent functions and their three models; Resurgent algebras: the multiplicative structure; The upper/lower Borel-Laplace transforms; Monomials in all four models; The pros and cons of the upper/lower choices
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2.2 Alien derivations as a tool for Riemann surface descriptionDefinition of the operators ω and ω; Lateral and median singularities; Compact description of Riemann surfaces; Strong versus weak resurgence; The pros and cons of the 2πi factor; 2.3 Retrieving the resurgence of a series from the resurgence of its Taylor coefficients; Retrieving closest singularities; Retrieving distant singularities; 3 The ingress factor; 3.1 Bernoulli numbers and polynomials; The Bernoulli numbers and polynomials; The Euler-MacLaurin formula; 3.2 Resurgence of the Gamma function
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3.3 Monomial/binomial/exponential factorsMonomial factors; Binomial factors; Exponential factors; 3.4 Resummability of the total ingress factor; 3.5 Parity relations; 4 Inner generators; 4.1 Some heuristics; 4.2 The long chain behind nir//mir; Details of the nine steps:; "Compact" and "layered" expansions of mir; 4.3 The nir transform; Integral expression of nir; 4.4 The reciprocation transform; 4.5 The mir transform; 4.6 Translocation of the nir transform; 4.7 Alternative factorisations of nir. The lir transform; 4.8 Application: kernel of the nir transform
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4.9 Comparing/extending/inverting nir and mir4.10 Parity relations; 5 Outer generators; 5.1 Some heuristics; 5.2 The short and long chains behind nur/mur; The short, four-link chain:; Details of the four steps:; The long, nine-link chain:; Details of the nine steps:; 5.3 The nur transform; 5.4 Expressing nur in terms of nir; 5.5 The mur transform; 5.6 Translocation of the nur transform; 5.7 Removal of the ingress factor; 5.8 Parity relations; 6 Inner generators and ordinary differential equations; 6.1 "Variable" and "covariant" differential equations
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Existence and calculation of the variable ODEs
Additional Edition:
ISBN 9788876423741
Additional Edition:
Buchausg. u.d.T. Asymptotics in dynamics, geometry and PDEs; generalized Borel summation ; 1 Pisa : Scuola Normale Superiore, 2011 ISBN 9788876423741
Language:
English
DOI:
10.1007/978-88-7642-379-6
URL:
Volltext
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URL:
Volltext
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