The Principle of Least Action in Geometry and Dynamics
Siburg, Karl Friedrich.
The Principle of Least Action in Geometry and Dynamics [electronic resource] / by Karl Friedrich Siburg. - XII, 132 p. online resource. - Lecture Notes in Mathematics, 1844 0075-8434 ; . - Lecture Notes in Mathematics, 1844 .
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.
9783540409854
10.1007/978-3-540-40985-4 doi
Differentiable dynamical systems.
Global differential geometry.
Global analysis.
Dynamical Systems and Ergodic Theory.
Differential Geometry.
Global Analysis and Analysis on Manifolds.
QA313
515.39 515.48
The Principle of Least Action in Geometry and Dynamics [electronic resource] / by Karl Friedrich Siburg. - XII, 132 p. online resource. - Lecture Notes in Mathematics, 1844 0075-8434 ; . - Lecture Notes in Mathematics, 1844 .
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.
9783540409854
10.1007/978-3-540-40985-4 doi
Differentiable dynamical systems.
Global differential geometry.
Global analysis.
Dynamical Systems and Ergodic Theory.
Differential Geometry.
Global Analysis and Analysis on Manifolds.
QA313
515.39 515.48