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Action-minimizing methods in Hamiltonian dynamics : an introduction to Aubry-Mather theory /
John Mather's seminal works in Hamiltonian dynamics represent some of the most important contributions to our understanding of the complex balance between stable and unstable motions in classical mechanics. His novel approach-known as Aubry-Mather theory-singles out the existence of special orb...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Princeton :
Princeton University Press,
[2015]
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| Colección: | Mathematical notes (Princeton University Press) ;
50. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 3.6 Holonomic Measures and Generic Properties of Tonelli Lagrangians4 Action-Minimizing Curves for Tonelli Lagrangians; 4.1 Global Action-Minimizing Curves: Aubry and Mañé Sets; 4.2 Some Topological and Symplectic Properties of the Aubry and Mañé Sets; 4.3 An Example: The Simple Pendulum (Part II); 4.4 Mather's Approach: Peierls' Barrier; 5 The Hamilton-Jacobi Equation and Weak KAM Theory; 5.1 Weak Solutions and Subsolutions of Hamilton-Jacobi and Fathi's Weak KAM theory; 5.2 Regularity of Critical Subsolutions; 5.3 Non-Wandering Points of the Mañé Set; Appendices.
- A On the Existence of Invariant Lagrangian GraphsA. 1 Symplectic Geometry of the Phase Space; A.2 Existence and Nonexistence of Invariant Lagrangian Graphs; B Schwartzman Asymptotic Cycle and Dynamics; B.1 Schwartzman Asymptotic Cycle; B.2 Dynamical Properties; Bibliography; Index.