Ebook: Critical Point Theory for Lagrangian Systems
Author: Marco Mazzucchelli (auth.)
- Tags: Mathematical Physics, Dynamical Systems and Ergodic Theory, Global Analysis and Analysis on Manifolds
- Series: Progress in Mathematics 293
- Year: 2012
- Publisher: Birkhäuser Basel
- Edition: 1
- Language: English
- pdf
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.
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.
Content:
Front Matter....Pages i-xii
Lagrangian and Hamiltonian Systems....Pages 1-27
The Morse Indices in Lagrangian Dynamics....Pages 29-48
Functional Setting for the Lagrangian Action....Pages 49-77
Discretizations....Pages 79-107
Local Homology and Hilbert Subspaces....Pages 109-125
Periodic Orbits of Tonelli Lagrangian Systems....Pages 127-156
Back Matter....Pages 157-187
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.
Content:
Front Matter....Pages i-xii
Lagrangian and Hamiltonian Systems....Pages 1-27
The Morse Indices in Lagrangian Dynamics....Pages 29-48
Functional Setting for the Lagrangian Action....Pages 49-77
Discretizations....Pages 79-107
Local Homology and Hilbert Subspaces....Pages 109-125
Periodic Orbits of Tonelli Lagrangian Systems....Pages 127-156
Back Matter....Pages 157-187
....