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024 7 $a10.1515/9781400866618
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035   $a(OCoLC)908080604
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035   $a(DE-B1597)9781400866618
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100   $a20150415h20152015  uy             0
101 0 $aeng
135   $aur|u---|u||u
181   $ctxt
182   $cc
183   $acr
200 10$aAction-minimizing methods in Hamiltonian dynamics $ean introduction to Aubry-Mather theory /$fAlfonso Sorrentino
205   $aPilot project,eBook available to selected US libraries only
210  1$aPrinceton, [New Jersey] ;$aOxford, [England] :$cPrinceton University Press,$d2015.
210  4$dİ2015
215   $a1 online resource (129 p.)
225 0 $aMathematical Notes ;$v50
300   $aDescription based upon print version of record.
311 0 $a0-691-16450-9 
311 0 $a1-4008-6661-8 
320   $aIncludes bibliographical references and index.
327   $tFront matter --$tContents --$tPreface --$tChapter One. Tonelli Lagrangians and Hamiltonians on Compact Manifolds --$tChapter Two. From KAM Theory to Aubry-Mather Theory --$tChapter Three. Action-Minimizing Invariant Measures for Tonelli Lagrangians --$tChapter Four. Action-Minimizing Curves for Tonelli Lagrangians --$tChapter Five. The Hamilton-Jacobi Equation and Weak KAM Theory --$tAppendices --$tAppendix A. On the Existence of Invariant Lagrangian Graphs --$tAppendix B. Schwartzman Asymptotic Cycle and Dynamics --$tBibliography --$tIndex
330   $aJohn Mather's seminal works in Hamiltonian dynamics represent some of the most important contributions to our understanding of the complex balance between stable and unstable motions in classical mechanics. His novel approach-known as Aubry-Mather theory-singles out the existence of special orbits and invariant measures of the system, which possess a very rich dynamical and geometric structure. In particular, the associated invariant sets play a leading role in determining the global dynamics of the system. This book provides a comprehensive introduction to Mather's theory, and can serve as an interdisciplinary bridge for researchers and students from different fields seeking to acquaint themselves with the topic.Starting with the mathematical background from which Mather's theory was born, Alfonso Sorrentino first focuses on the core questions the theory aims to answer-notably the destiny of broken invariant KAM tori and the onset of chaos-and describes how it can be viewed as a natural counterpart of KAM theory. He achieves this by guiding readers through a detailed illustrative example, which also provides the basis for introducing the main ideas and concepts of the general theory. Sorrentino then describes the whole theory and its subsequent developments and applications in their full generality.Shedding new light on John Mather's revolutionary ideas, this book is certain to become a foundational text in the modern study of Hamiltonian systems.
410  0$aMathematical notes (Princeton University Press) ;$v50.
606   $aHamiltonian systems
606   $aHamilton-Jacobi equations
610   $aAlbert Fathi.
610   $aAubry set.
610   $aAubry?ather theory.
610   $aHamiltonian dynamics.
610   $aHamiltonians.
610   $aHamilton?acobi equation.
610   $aJohn Mather.
610   $aKAM theory.
610   $aKAM tori.
610   $aLagrangian dynamics.
610   $aMAK tori.
610   $aMa set.
610   $aMa's critical value.
610   $aMa's potential.
610   $aMaher sets.
610   $aPeierls' barrier.
610   $aTonelli Lagrangians.
610   $aaction-minimizing measure.
610   $aaction-minimizing orbits.
610   $achaos.
610   $aclassical mechanics.
610   $acompact manifold.
610   $adifferentiability.
610   $ainvariant Lagrangian graphs.
610   $ainvariant probability measures.
610   $ainvariant sets.
610   $aorbits.
610   $apendulum.
610   $astable motion.
610   $astrict convexity.
610   $aunstable motion.
615  0$aHamiltonian systems.
615  0$aHamilton-Jacobi equations.
676   $a514.74
700   $aSorrentino$b Alfonso$01685268
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910812171703321
996   $aAction-minimizing methods in Hamiltonian dynamics$94057274
997   $aUNINA