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Applications of Centre Manifold Theory

  • Book
  • © 1982

Overview

Authors:
  1. Jack Carr

    1. Department of Mathematics, Heriot-Watt University, Edinburgh, Scotland

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Part of the book series: Applied Mathematical Sciences (AMS, volume 35)

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Table of contents (6 chapters)

  1. Front Matter

    Pages iii-xiV
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  2. Introduction to Centre Manifold Theory

    • Jack Carr
    Pages 1-13

  3. Proofs of Theorems

    • Jack Carr
    Pages 14-36

  4. Examples

    • Jack Carr
    Pages 37-53

  5. Bifurcations with Two Parameters in Two Dimensions

    • Jack Carr
    Pages 54-87

  6. Application to a Panel Flutter Problem

    • Jack Carr
    Pages 88-96

  7. Infinite Dimensional Problems

    • Jack Carr
    Pages 97-135

  8. Back Matter

    Pages 136-142
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Keywords

About this book

These notes are based on a series of lectures given in the Lefschetz Center for Dynamical Systems in the Division of Applied Mathematics at Brown University during the academic year 1978-79. The purpose of the lectures was to give an introduction to the applications of centre manifold theory to differential equations. Most of the material is presented in an informal fashion, by means of worked examples in the hope that this clarifies the use of centre manifold theory. The main application of centre manifold theory given in these notes is to dynamic bifurcation theory. Dynamic bifurcation theory is concerned with topological changes in the nature of the solutions of differential equations as para­ meters are varied. Such an example is the creation of periodic orbits from an equilibrium point as a parameter crosses a critical value. In certain circumstances, the application of centre manifold theory reduces the dimension of the system under investigation. In this respect the centre manifold theory plays the same role for dynamic problems as the Liapunov-Schmitt procedure plays for the analysis of static solutions. Our use of centre manifold theory in bifurcation problems follows that of Ruelle and Takens [57) and of Marsden and McCracken [51).

Authors and Affiliations

  • Department of Mathematics, Heriot-Watt University, Edinburgh, Scotland

    Jack Carr

Bibliographic Information

  • Book Title: Applications of Centre Manifold Theory

  • Authors: Jack Carr

  • Series Title: Applied Mathematical Sciences

  • DOI: https://doi.org/10.1007/978-1-4612-5929-9

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York Inc. 1982

  • Softcover ISBN: 978-0-387-90577-8Published: 29 June 1981

  • eBook ISBN: 978-1-4612-5929-9Published: 06 December 2012

  • Series ISSN: 0066-5452

  • Series E-ISSN: 2196-968X

  • Edition Number: 1

  • Number of Pages: XIV, 142

  • Topics: Manifolds and Cell Complexes (incl. Diff.Topology)

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