Critical Point Theory for Lagrangian Systems [electronic resource] / by Marco Mazzucchelli.
Contributor(s): SpringerLink (Online service)Material type: TextSeries: Progress in Mathematics: 293Publisher: Basel : Springer Basel, 2012Description: XII, 188 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783034801638Subject(s): Mathematics | Dynamics | Ergodic theory | Global analysis (Mathematics) | Manifolds (Mathematics) | Mathematical physics | Mathematics | Mathematical Physics | Dynamical Systems and Ergodic Theory | Global Analysis and Analysis on ManifoldsAdditional physical formats: Printed edition:: No titleDDC classification: 530.15 LOC classification: QA401-425QC19.2-20.85Online resources: Click here to access online
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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.