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Hamiltonian and Lagrangian Flows on Center Manifolds

with Applications to Elliptic Variational Problems

  • Authors
  • Alexander Mielke

Part of the Lecture Notes in Mathematics book series (LNM, volume 1489)

Table of contents

  1. Front Matter
    Pages I-X
  2. Alexander Mielke
    Pages 1-6
  3. Alexander Mielke
    Pages 9-16
  4. Alexander Mielke
    Pages 17-26
  5. Alexander Mielke
    Pages 27-40
  6. Alexander Mielke
    Pages 41-59
  7. Alexander Mielke
    Pages 61-83
  8. Alexander Mielke
    Pages 85-92
  9. Alexander Mielke
    Pages 103-108
  10. Alexander Mielke
    Pages 109-119
  11. Alexander Mielke
    Pages 121-131
  12. Back Matter
    Pages 133-142

About this book

Introduction

The theory of center manifold reduction is studied in this monograph in the context of (infinite-dimensional) Hamil- tonian and Lagrangian systems. The aim is to establish a "natural reduction method" for Lagrangian systems to their center manifolds. Nonautonomous problems are considered as well assystems invariant under the action of a Lie group ( including the case of relative equilibria). The theory is applied to elliptic variational problemson cylindrical domains. As a result, all bounded solutions bifurcating from a trivial state can be described by a reduced finite-dimensional variational problem of Lagrangian type. This provides a rigorous justification of rod theory from fully nonlinear three-dimensional elasticity. The book will be of interest to researchers working in classical mechanics, dynamical systems, elliptic variational problems, and continuum mechanics. It begins with the elements of Hamiltonian theory and center manifold reduction in order to make the methods accessible to non-specialists, from graduate student level.

Keywords

Bifurcation Center Manifold Hamiltonian and Langrangian Systems Lie group Nonlinear Elasticity Variational Problems classical mechanics manifold

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0097544
  • Copyright Information Springer-Verlag Berlin Heidelberg 1991
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-54710-5
  • Online ISBN 978-3-540-46441-9
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site
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