Progress in Mathematics

Critical Point Theory for Lagrangian Systems

Authors: Mazzucchelli, Marco

  • Collects, in a rigorous and consistent style, many important results that are sparse in the literature
  • Exposition is self-contained
  • Arguments are presented in an elementary way in order to be accessible to the non-specialists
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About this book

Lagrangian systems constitute a very important and old class in dynamics. Their origin dates back to the end of the eighteenth century, with Joseph-Louis Lagrange’s reformulation of classical mechanics. The main feature of Lagrangian dynamics is its variational flavor: orbits are extremal points of an action functional. The development of critical point theory in the twentieth century provided a powerful machinery to investigate existence and multiplicity questions for orbits of Lagrangian systems. This monograph gives a modern account of the application of critical point theory, and more specifically Morse theory, to Lagrangian dynamics, with particular emphasis toward existence and multiplicity of periodic orbits of non-autonomous and time-periodic systems.

Reviews

From the reviews:

“This monograph concerns the use of critical point theory tools in connection with questions of existence and multiplicity of periodic solutions of Lagrangian systems. … The monograph contains several proofs and seems to be especially suitable for researchers and advanced graduate students interested in applications of critical point theory to boundary value problems for Lagrangian systems.” (Maria Letizia Bertotti, Mathematical Reviews, September, 2013)

“The results of critical point theory provide powerful techniques to investigate and study aspects of Lagrangian systems such as existence, multiplicity or uniqueness of solutions of the Euler-Lagrange equations with prescribed boundary conditions. … A bibliography with 88 entries, a list of symbols distributed on each chapter, and a subject index complete the work. The book is self-contained and rigorously presented. Various aspects of it should be of interest to graduate students and researchers in this dynamic field of mathematics.” (Dorin Andrica, Zentralblatt MATH, Vol. 1246, 2012)


Table of contents (6 chapters)

  • Lagrangian and Hamiltonian Systems

    Mazzucchelli, Marco

    Pages 1-27

  • The Morse Indices in Lagrangian Dynamics

    Mazzucchelli, Marco

    Pages 29-48

  • Functional Setting for the Lagrangian Action

    Mazzucchelli, Marco

    Pages 49-77

  • Discretizations

    Mazzucchelli, Marco

    Pages 79-107

  • Local Homology and Hilbert Subspaces

    Mazzucchelli, Marco

    Pages 109-125

Buy this book

eBook $99.00
price for USA (gross)
  • ISBN 978-3-0348-0163-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $129.00
price for USA
  • ISBN 978-3-0348-0162-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $129.00
price for USA
  • ISBN 978-3-0348-0782-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Critical Point Theory for Lagrangian Systems
Authors
Series Title
Progress in Mathematics
Series Volume
293
Copyright
2012
Publisher
Birkhäuser Basel
Copyright Holder
Springer Basel AG
eBook ISBN
978-3-0348-0163-8
DOI
10.1007/978-3-0348-0163-8
Hardcover ISBN
978-3-0348-0162-1
Softcover ISBN
978-3-0348-0782-1
Series ISSN
0743-1643
Edition Number
1
Number of Pages
XII, 188
Topics