Critical Point Theory for Lagrangian Systems /
by Marco Mazzucchelli.
- xii, 187 páginas 1 ilustraciones en color. recurso en línea.
- Progress in Mathematics ; 293 .
Springer eBooks
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.
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.