Divergent Series, Summability and Resurgence I-III

ISBN-13: 9783319595276 / Angielski / Miękka / 1

Eric Delabaere; Michele Loday-Richaud; Claude Mitschi

Spis treści

Preface.-Preface to the three volumes.- Part I:Monodromy in Linear Differential Equations.- 1 analytic continuation and monodromy.- Differential Galois Theory.- Inverse Problems.- The Riemann-Hilbert problem.- Part II: Introduction to 1-Summability and Resurgence.- 5 Borel-Laplace Summation.- Resurgent Functions and Alien Calculus.- the Resurgent Viewpoint on Holomorphic Tangent-to-Identity Germs.- Acknowledgements.- Index.

Avant-propos.- Preface to the three volumes.- Introduction to this volume.- 1 Asymptotic Expansions in the Complex Domain.- 2 Sheaves and Čech cohomology.- 3 Linear Ordinary Differential Equations.- 4 Irregularity and Gevrey Index Theorems.- 5 Four Equivalent Approaches to k-Summability.- 6 Tangent-to-Identity Diffeomorphisms.- 7 Six Equivalent Approaches to Multisummability.- Exercises.- Solutions to Exercises.- Index.- Glossary of Notations.- References.

Avant-Propos.- Preface to the three volumes.- Preface to this volume.- Some elements about ordinary differential equations.- The first Painlevé equation.-  Tritruncated solutions for the first Painlevé equation.- A step beyond Borel-Laplace summability.- Transseries and formal integral for the first Painlevé equation.- Truncated solutions for the first Painlevé equation.- Supplements to resurgence theory.- Resurgent structure for the first Painlevé equation.- Index.