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.
The Principle of Least Action in Geometry and Dynamics
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Inside This Book
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First Sentence:
The Principle of Least Action states that, for sufficiently short times, trajectories of a Lagrangian system minimize the action amongst all paths in configuration space with the same end points. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
length spectrum invariant, monotone twist map, foliation cycles, convex caustics, graph selector, marked length spectrum, integrable twist map, billiard map, minimal orbits, convex billiards, twist interval, boundary rigidity, minimal action, minimizing hypersurface, regular level set, characteristic foliation, convex conjugate, elliptic fixed point, minimizing measures, strictly convex domain, invariant circles, twist maps, twist mappings, minimal geodesic, elliptical billiard Key Phrases - Capitalized Phrases (CAPs): (learn more)
Aubry Mather, Main Principle, Nova Ser New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
The Principle of Least Action states that, for sufficiently short times, trajectories of a Lagrangian system minimize the action amongst all paths in configuration space with the same end points. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
length spectrum invariant, monotone twist map, foliation cycles, convex caustics, graph selector, marked length spectrum, integrable twist map, billiard map, minimal orbits, convex billiards, twist interval, boundary rigidity, minimal action, minimizing hypersurface, regular level set, characteristic foliation, convex conjugate, elliptic fixed point, minimizing measures, strictly convex domain, invariant circles, twist maps, twist mappings, minimal geodesic, elliptical billiard Key Phrases - Capitalized Phrases (CAPs): (learn more)
Aubry Mather, Main Principle, Nova Ser New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 94
books:
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15
books
cite this book:
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- Forward-Backward Stochastic Differential Equations and their Applications (Lecture Notes in Mathematics) by Jin Ma in Back Matter (1), and Back Matter (2)
- Geometric Curve Evolution and Image Processing (Lecture Notes in Mathematics) by Frédéric Cao in Back Matter
- Big Queues (Lecture Notes in Mathematics) by Ayalvadi J. Ganesh in Back Matter
- Grothendieck Duality and Base Change (Lecture Notes in Mathematics) by Brian Conrad in Back Matter
- Notes on Infinite Permutation Groups (Lecture Notes in Mathematics) by Meenaxi Bhattacharjee in Back Matter
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- Quantum Independent Increment Processes I: From Classical Probability to Quantum Stochastic Calculus (Lecture Notes in Mathematics) (v. 1) by David Applebaum in Back Matter
- Quantum Independent Increment Processes II: Structure of Quantum Lévy Processes, Classical Probability, and Physics (Lecture Notes in Mathematics) (v. 2) by Ole Eiler Barndorff-Nielsen in Back Matter
- Statistical Learning Theory and Stochastic Optimization: Ecole d'Eté de Probabilités de Saint-Flour XXXI - 2001 (Lecture Notes in Mathematics) by Olivier Catoni in Back Matter
- Mixed Automorphic Forms, Torus Bundles, and Jacobi Forms (Lecture Notes in Mathematics) by Min Ho Lee in Back Matter
- Fourier Transforms of Invariant Functions on Finite Reductive Lie Algebras (Lecture Notes in Mathematics) by Emmanuel Letellier in Back Matter
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