Divergent Series, Summability and Resurgence I : Monodromy and Resurgence / by Claude Mitschi, David Sauzin.

Format:

Book

Author/Creator:

Mitschi, Claude., Author.

Sauzin, David., Author.

Series:

Lecture Notes in Mathematics, 0075-8434 ; 2153

Language:

English

Subjects (All):

Differential equations.

Sequences (Mathematics).

Difference equations.

Functional equations.

Dynamics.

Ergodic theory.

Topological groups.

Lie groups.

Ordinary Differential Equations.

Sequences, Series, Summability.

Difference and Functional Equations.

Dynamical Systems and Ergodic Theory.

Topological Groups, Lie Groups.

Local Subjects:

Ordinary Differential Equations.

Sequences, Series, Summability.

Difference and Functional Equations.

Dynamical Systems and Ergodic Theory.

Topological Groups, Lie Groups.

Physical Description:

1 online resource (XXI, 298 p. 24 illus., 19 illus. in color.)

Edition:

1st ed. 2016.

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2016.

Summary:

Providing an elementary introduction to analytic continuation and monodromy, the first part of this volume applies these notions to the local and global study of complex linear differential equations, their formal solutions at singular points, their monodromy and their differential Galois groups. The Riemann-Hilbert problem is discussed from Bolibrukh’s point of view. The second part expounds 1-summability and Ecalle’s theory of resurgence under fairly general conditions. It contains numerous examples and presents an analysis of the singularities in the Borel plane via “alien calculus”, which provides a full description of the Stokes phenomenon for linear or non-linear differential or difference equations. The first of a series of three, entitled Divergent Series, Summability and Resurgence, this volume is aimed at graduate students, mathematicians and theoretical physicists interested in geometric, algebraic or local analytic properties of dynamical systems. It includes useful exercises with solutions. The prerequisites are a working knowledge of elementary complex analysis and differential algebra.

Contents:

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.

ISBN:

3-319-28736-2