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 Lagrangiandynamics 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. INDICE: 1 Lagrangian and Hamiltonian systems. 2 Functional setting for theLagrangian 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.
- ISBN: 978-3-0348-0162-1
- Editorial: Springer Basel
- Encuadernacion: Cartoné
- Páginas: 180
- Fecha Publicación: 31/08/2011
- Nº Volúmenes: 1
- Idioma: Inglés