rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Divergent Series, Summability and Resurgence I
    sub title: Monodromy and Resurgence
  name:
    name part: Mitschi, Claude.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Sauzin, David.
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2016
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XXI, 298 p. 24 illus., 19 illus. in color. online resource.
  abstract: 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.
  table of 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.
  note: by Claude Mitschi, David Sauzin.
  subject:
    topic: Mathematics
  subject:
    topic: Topological groups
  subject:
    topic: Lie groups
  subject:
    topic: Difference equations
  subject:
    topic: Functional equations
  subject:
    topic: Dynamics
  subject:
    topic: Ergodic theory
  subject:
    topic: Differential equations
  subject:
    topic: Sequences (Mathematics)
  subject:
    topic: Mathematics
  subject:
    topic: Ordinary Differential Equations
  subject:
    topic: Sequences, Series, Summability
  subject:
    topic: Difference and Functional Equations
  subject:
    topic: Dynamical Systems and Ergodic Theory
  subject:
    topic: Topological Groups, Lie Groups
  classification: QA372
  classification: 515.352
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Lecture Notes in Mathematics, 2153
  identifier: 9783319287362
  identifier: http://dx.doi.org/10.1007/978-3-319-28736-2
  record info:
    record creation date: 160827
    record change date: 20160827141108.0
    record identifier: 978-3-319-28736-2