The principle of least action in geometry and dynamics / Karl Friedrich Siburg.Material type: TextSeries: Lecture notes in mathematics (Springer-Verlag) ; 1844.Publication details: Berlin ; New York : Springer-Verlag, ©2004. Description: 1 online resource (xii, 128 pages) : illustrationsContent type: text Media type: computer Carrier type: online resourceISBN: 3540219447; 9783540219446; 9783540409854; 3540409858Subject(s): Symplectic manifolds | Geometry, Differential | Geometry, Differential | Symplectic manifoldsGenre/Form: Electronic books. | Electronic books. Additional physical formats: Print version:: Principle of least action in geometry and dynamics.DDC classification: 510 s | 516.3/5 LOC classification: QA649 | .S52 2004Online resources: Click here to access online
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Includes bibliographical references and index.
Print version record.
Aubry-Mather Theory -- Mather-Mané Theory -- The Minimal Action and Convex Billiards -- The Minimal Action Near Fixed Points and Invariant Tori -- The Minimal Action and Hofer's Geometry -- The Minimal Action and Symplectic Geometry -- References -- Index.
New variational methods by Aubry, Mather, and Mane, discovered in the last twenty years, gave deep insight into the dynamics of convex Lagrangian systems. This book shows how this Principle of Least Action appears in a variety of settings (billiards, length spectrum, Hofer geometry, modern symplectic geometry). Thus, topics from modern dynamical systems and modern symplectic geometry are linked in a new and sometimes surprising way. The central object is Mather's minimal action functional. The level is for graduate students onwards, but also for researchers in any of the subjects touched in the book.