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Hamiltonian and Lagrangian Flows on Center Manifolds

with Applications to Elliptic Variational Problems

  • Book
  • © 1991

Overview

Authors:
  1. Alexander Mielke
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1489)

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Table of contents (11 chapters)

  1. Front Matter

    Pages I-X
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  2. Introduction

    • Alexander Mielke
    Pages 1-6

  3. Notations and basic facts on center manifolds

    • Alexander Mielke
    Pages 9-16

  4. The linear theory

    • Alexander Mielke
    Pages 17-26

  5. Hamiltonian flows on center manifolds

    • Alexander Mielke
    Pages 27-40

  6. Hamiltonian systems with symmetries

    • Alexander Mielke
    Pages 41-59

  7. Lagrangian systems

    • Alexander Mielke
    Pages 61-83

  8. Nonautonomous systems

    • Alexander Mielke
    Pages 85-92

  9. Elliptic variational problems on cylindrical domains

    • Alexander Mielke
    Pages 95-102

  10. Capillarity surface waves

    • Alexander Mielke
    Pages 103-108

  11. Necking of strips

    • Alexander Mielke
    Pages 109-119

  12. Saint-Venant's problem

    • Alexander Mielke
    Pages 121-131

  13. Back Matter

    Pages 133-142
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Keywords

About this book

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.

Bibliographic Information

  • Book Title: Hamiltonian and Lagrangian Flows on Center Manifolds

  • Book Subtitle: with Applications to Elliptic Variational Problems

  • Authors: Alexander Mielke

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0097544

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1991

  • Softcover ISBN: 978-3-540-54710-5Published: 23 October 1991

  • eBook ISBN: 978-3-540-46441-9Published: 14 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: X, 140

  • Topics: Analysis, Theoretical, Mathematical and Computational Physics

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