| Description |
1 online resource (384 pages) |
| Series |
Contemporary Mathematics ; v. 373 |
|
Contemporary Mathematics
|
| Contents |
Contents -- Preface -- A singularly perturbed Riccati equation -- On global aspects of exact WKB analysis of operators admitting infinitely many phases -- Asymptotic differential algebra -- Introduction -- 1. Hardy Fields -- 2. The Field of Logarithmic-Exponential Series -- 3. H-Fields and Asymptotic Couples -- 4. Algebraic Differential Equations over H-Fields -- References -- Formally well-posed Cauchy problems for linear partial differential equations with constant coefficients -- Non-oscillating integral curves and O-minimal structures -- 1. Introduction |
|
2. Definitions and examples2.1 Hardy fields and o-minimal structures -- 2.2 Boshernitzan's example -- 2.3 Quasianalytic Denjoy-Carleman classes -- 3. Euler's equation -- 3.1 Euler's equation in the real plane -- 3.2 Euler's equation in the complex plane -- 3.3 Formal conjugation -- Asymptotics and singularities for a class of difference equations -- Topological construction of transseries and introduction to generalized Borel summability -- 1. Introduction -- 1.1. Abstract multiseries -- 1.2. Topology on multiseries -- 1.3. Contractive operators |
|
1.4. Inductive construction of logarithm-free transseries1.5. The space T of general transseries -- 2. Equations in T: examples -- 2.1. Multidimensional systems: transseries solutions at irregular singularities of rank one -- 3. Borel summation techniques -- 3.1. Borel summation of transseries: a first order example -- 3.2. Generalized Borel summation for rank one ODEs -- 3.3. Difference equations and PDEs -- 3.4. More general irregular singularities and multisummability -- References -- Addendum to the hyperasymptotics for multidimensional Laplace integrals |
|
Higher-order terms for the de Moivre-Laplace theoremTwisted resurgence monomials and canonical-spherical synthesis of local objects -- 1. Introduction: Object Analysis and Object Synthesis -- 1.1 The notion of Local Analytic Object -- 1.2 Object Analysis: the Bridge Equation -- 1.3 Object Synthesis: semi-formal candidates -- 1.4 Object Synthesis: from semi-formal to effective -- 2. Reminders about moulds, resurgent functions, alien derivations -- 2.1 Moulds/comoulds -- 2.2 Resurgent functions -- 2.3 Alien derivations or automorphisms. Their weights |
|
2.4 Resurgence monomials3. Object Analysis: six basic examples -- 3.1 Example 1: shift-like diffeomorphism -- 3.2 Example 2: Euler-like differential equation -- 3.3 Example 3: monocritical linear differential system -- 3.4 Example 4: monocritical non-linear differential system -- 3.5 Example 5: polycritical linear differential system -- 3.6 Example 6: polycritical non-linear differential system -- 4. The reverse problem: Object Synthesis -- 4.1 Standard or hyperlogarithmic resurgence monomials and monics -- 4.2 Semi-formal synthesis in Example 1 |
| Notes |
""4.3 Semi-formal synthesis in Example 2"" |
|
Print version record |
| Subject |
Asymptotic expansions -- Congresses
|
|
Functions -- Congresses
|
|
Asymptotic expansions.
|
|
Functions.
|
| Genre/Form |
Conference papers and proceedings.
|
| Form |
Electronic book
|
| Author |
Kruskal, M. D
|
|
Macintyre, A
|
| ISBN |
9780821879634 |
|
0821879634 |
|
