Critical Point Theory for Lagrangian 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.

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.

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 Includes supplementary material: sn.pub/extras

Inhalt
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.