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AuthorSiburg, Karl Friedrich. author
TitleThe Principle of Least Action in Geometry and Dynamics [electronic resource] / by Karl Friedrich Siburg
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2004
Connect tohttp://dx.doi.org/10.1007/978-3-540-40985-4
Descript XII, 132 p. online resource

SUMMARY

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


CONTENT

Aubry-Mather Theory -- Mather-Manรฉ 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


Mathematics Dynamics Ergodic theory Global analysis (Mathematics) Manifolds (Mathematics) Differential geometry Mathematics Dynamical Systems and Ergodic Theory Differential Geometry Global Analysis and Analysis on Manifolds



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