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: Normal Forms and Unfoldings for Local Dynamical Systems
  name:
    name part: Murdock, James.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: xxu
    date issued: 2003
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XX, 500 p. online resource.
  abstract: The subject of local dynamical systems is concerned with the following two questions: 1. Given an n×n matrix A, describe the behavior, in a neighborhood of the origin, of the solutions of all systems of di?erential equations having a rest point at the origin with linear part Ax, that is, all systems of the form x ? = Ax+··· , n where x? R and the dots denote terms of quadratic and higher order. 2. Describethebehavior(neartheorigin)ofallsystemsclosetoasystem of the type just described. To answer these questions, the following steps are employed: 1. A normal form is obtained for the general system with linear part Ax. The normal form is intended to be the simplest form into which any system of the intended type can be transformed by changing the coordinates in a prescribed manner. 2. An unfolding of the normal form is obtained. This is intended to be the simplest form into which all systems close to the original s- tem can be transformed. It will contain parameters, called unfolding parameters, that are not present in the normal form found in step 1. vi Preface 3. The normal form, or its unfolding, is truncated at some degree k, and the behavior of the truncated system is studied.
  table of contents: Preface -- 1. Two Examples -- 2. The splitting problem for linear operators -- 3. Linear Normal Forms -- 4. Nonlinear Normal Forms -- 5. Geometrical Structures in Normal Forms -- 6. Selected Topics in Local Bifurcation Theory -- Appendix A: Rings -- Appendix B: Modules -- Appendix C: Format 2b: Generated Recursive (Hori) -- Appendix D: Format 2c: Generated Recursive (Deprit) -- Appendix E: On Some Algorithms in Linear Algebra -- Bibliography -- Index.
  note: by James Murdock.
  subject:
    topic: Mathematics
  subject:
    topic: Differential equations
  subject:
    topic: Applied mathematics
  subject:
    topic: Engineering mathematics
  subject:
    topic: Physics
  subject:
    topic: Mathematics
  subject:
    topic: Ordinary Differential Equations
  subject:
    topic: Applications of Mathematics
  subject:
    topic: Theoretical, Mathematical and Computational Physics
  classification: QA372
  classification: 515.352
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Springer Monographs in Mathematics
  identifier: 9780387217857
  identifier: http://dx.doi.org/10.1007/b97515
  record info:
    record creation date: 121227
    record change date: 20151116134050.0
    record identifier: 978-0-387-21785-7