Sorrentino, Alfonso, 1979-
Action-minimizing methods in Hamiltonian dynamics : an introduction to Aubry-Mather theory / Alfonso Sorrentino. - 1 online resource (xi, 115 pages) - Mathematical notes ; 50 . - Mathematical notes (Princeton University Press) ; 50. .
Includes bibliographical references and index.
3.6 Holonomic Measures and Generic Properties of Tonelli Lagrangians4 Action-Minimizing Curves for Tonelli Lagrangians; 4.1 Global Action-Minimizing Curves: Aubry and Ma�n�e Sets; 4.2 Some Topological and Symplectic Properties of the Aubry and Ma�n�e 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 Ma�n�e 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.
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 orbits and invariant measures of the system, which possess a very rich dynamical and geometric structure. In particular, the associated invariant sets play a leading role in determining the global dynamics of the system. This book provides a comprehensive introduction to Mather's theory, and can serve as an interdisciplinary bridge for researchers and students from different fields seeking to acquaint themselves with the topic.
9781400866618 1400866618
22573/ctt1b9wf38 JSTOR 9452421 IEEE
Hamiltonian systems.
Hamilton-Jacobi equations.
Syst�emes hamiltoniens.
�Equations de Hamilton-Jacobi.
MATHEMATICS--Calculus.
MATHEMATICS--Mathematical Analysis.
MATHEMATICS--General.
Hamilton-Jacobi equations.
Hamiltonian systems.
Electronic book.
Electronic books.
Electronic books.
QA614.83
515/.39
Action-minimizing methods in Hamiltonian dynamics : an introduction to Aubry-Mather theory / Alfonso Sorrentino. - 1 online resource (xi, 115 pages) - Mathematical notes ; 50 . - Mathematical notes (Princeton University Press) ; 50. .
Includes bibliographical references and index.
3.6 Holonomic Measures and Generic Properties of Tonelli Lagrangians4 Action-Minimizing Curves for Tonelli Lagrangians; 4.1 Global Action-Minimizing Curves: Aubry and Ma�n�e Sets; 4.2 Some Topological and Symplectic Properties of the Aubry and Ma�n�e 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 Ma�n�e 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.
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 orbits and invariant measures of the system, which possess a very rich dynamical and geometric structure. In particular, the associated invariant sets play a leading role in determining the global dynamics of the system. This book provides a comprehensive introduction to Mather's theory, and can serve as an interdisciplinary bridge for researchers and students from different fields seeking to acquaint themselves with the topic.
9781400866618 1400866618
22573/ctt1b9wf38 JSTOR 9452421 IEEE
Hamiltonian systems.
Hamilton-Jacobi equations.
Syst�emes hamiltoniens.
�Equations de Hamilton-Jacobi.
MATHEMATICS--Calculus.
MATHEMATICS--Mathematical Analysis.
MATHEMATICS--General.
Hamilton-Jacobi equations.
Hamiltonian systems.
Electronic book.
Electronic books.
Electronic books.
QA614.83
515/.39