Critical Point Theory for Lagrangian Systems [Hardcover]

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 Lagranges 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 investigateexistence 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.Here is a modern account of the application of critical point theory, specifically Morse theory, to Lagrangian dynamics, with particular emphasis on the existence and multiplicity of periodic orbits of non-autonomous and time-periodic systems.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.

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-Lagral£O