Mazzucchelli, Marco.
Critical Point Theory for Lagrangian Systems [electronic resource] / by Marco Mazzucchelli. - XII, 188 p. online resource. - Progress in Mathematics ; 293 . - Progress in Mathematics ; 293 .
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.
9783034801638
10.1007/978-3-0348-0163-8 doi
Mathematics.
Differentiable dynamical systems.
Global analysis.
Mathematics.
Mathematical Physics.
Dynamical Systems and Ergodic Theory.
Global Analysis and Analysis on Manifolds.
QA401-425 QC19.2-20.85
530.15
Critical Point Theory for Lagrangian Systems [electronic resource] / by Marco Mazzucchelli. - XII, 188 p. online resource. - Progress in Mathematics ; 293 . - Progress in Mathematics ; 293 .
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.
9783034801638
10.1007/978-3-0348-0163-8 doi
Mathematics.
Differentiable dynamical systems.
Global analysis.
Mathematics.
Mathematical Physics.
Dynamical Systems and Ergodic Theory.
Global Analysis and Analysis on Manifolds.
QA401-425 QC19.2-20.85
530.15