Mazzucchelli Critical Point Theory for Lagrangian Systems

1. Auflage 2011
ISBN: 978-3-0348-0163-8
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 188 Seiten, Web PDF

Reihe: Mathematics and Statistics

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.

Zielgruppe

Research

Autoren/Hrsg.

Mazzucchelli, Marco

Inhaltsverzeichnis

1 Lagrangian and Hamiltonian systems.- 2 Functional setting for the Lagrangian action.- 3 Discretizations.- 4 Local homology and Hilbert subspaces.- 5 Periodic orbits of Tonelli Lagrangian systems.- A An overview of Morse theory.-Bibliography.- List of symbols.- Index.