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| 049 | _aMAIN | ||
| 100 | 1 |
_aSorrentino, Alfonso, _d1979- _eauthor. _964326 |
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| 245 | 1 | 0 |
_aAction-minimizing methods in Hamiltonian dynamics : _ban introduction to Aubry-Mather theory / _cAlfonso Sorrentino. |
| 264 | 1 |
_aPrinceton : _bPrinceton University Press, _c[2015] |
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| 264 | 4 | _c�2015 | |
| 300 | _a1 online resource (xi, 115 pages) | ||
| 336 |
_atext _btxt _2rdacontent |
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| 337 |
_acomputer _bc _2rdamedia |
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| 338 |
_aonline resource _bcr _2rdacarrier |
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| 490 | 1 |
_aMathematical notes ; _v50 |
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| 504 | _aIncludes bibliographical references and index. | ||
| 588 | 0 | _aPrint version record. | |
| 505 | 8 |
_6880-01 _a3.6 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. |
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| 505 | 8 | _aA 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. | |
| 520 | _aJohn 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. | ||
| 590 |
_aIEEE _bIEEE Xplore Princeton University Press eBooks Library |
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| 650 | 0 |
_aHamiltonian systems. _912039 |
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| 650 | 0 |
_aHamilton-Jacobi equations. _964327 |
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| 650 | 6 |
_aSyst�emes hamiltoniens. _964328 |
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| 650 | 6 |
_a�Equations de Hamilton-Jacobi. _964329 |
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| 650 | 7 |
_aMATHEMATICS _xCalculus. _2bisacsh _916300 |
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| 650 | 7 |
_aMATHEMATICS _xMathematical Analysis. _2bisacsh _916301 |
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| 650 | 7 |
_aMATHEMATICS _xGeneral. _2bisacsh _94635 |
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| 650 | 7 |
_aHamilton-Jacobi equations. _2fast _0(OCoLC)fst00950768 _964327 |
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| 650 | 7 |
_aHamiltonian systems. _2fast _0(OCoLC)fst00950772 _912039 |
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| 655 | 0 |
_aElectronic book. _97794 |
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| 655 | 4 |
_aElectronic books. _93294 |
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| 655 | 7 |
_aElectronic books. _2lcgft _93294 |
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| 776 | 0 | 8 |
_iPrint version: _aSorrentino, Alfonso. _tAction-minimizing Methods in Hamiltonian Dynamics: An Introduction to Aubry-Mather Theory. _dPrinceton : Princeton University Press, �2015 _z9780691164502 |
| 830 | 0 |
_aMathematical notes (Princeton University Press) ; _v50. _964330 |
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| 856 | 4 | 0 | _uhttps://ieeexplore.ieee.org/servlet/opac?bknumber=9452421 |
| 880 | 0 |
_6505-01/(S _aCover; Copyright; Title; Contents; Preface; 1 Tonelli Lagrangians and Hamiltonians on Compact Manifolds; 1.1 Lagrangian Point of View; 1.2 Hamiltonian Point of View; 2 From KAM Theory to Aubry-Mather Theory; 2.1 Action-Minimizing Properties of Measures and Orbits on KAM Tori; 3 Action-Minimizing Invariant Measures for Tonelli Lagrangians; 3.1 Action-Minimizing Measures and Mather Sets; 3.2 Mather Measures and Rotation Vectors; 3.3 Mather's (Sa(B- and (Sb(B-Functions ; 3.4 The Symplectic Invariance of Mather Sets; 3.5 An Example: The Simple Pendulum (Part I). |
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