The Principle of Least Action in Geometry and Dynamics [electronic resource] / by Karl Friedrich Siburg.

By: Siburg, Karl Friedrich [author.]Contributor(s): SpringerLink (Online service)Material type: TextTextSeries: Lecture Notes in Mathematics ; 1844Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2004Description: XII, 132 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783540409854Subject(s): Mathematics | Differentiable dynamical systems | Global analysis | Global differential geometry | Mathematics | Dynamical Systems and Ergodic Theory | Differential Geometry | Global Analysis and Analysis on ManifoldsAdditional physical formats: Printed edition:: No titleDDC classification: 515.39 | 515.48 LOC classification: QA313Online resources: Click here to access online
Contents:
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.
In: Springer eBooksSummary: 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.
Item type: E-BOOKS
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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.

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