MARC record from Internet Archive

LEADER: 03095cam a2200397 a 4500
001 013000259-3
005 20140910154305.0
008 111216s2011 nyua b 001 0 eng c
016 7 $a015869348$2Uk
020 $a9781461414988
020 $a1461414989
035 0 $aocn768491382
040 $aPAU$cPAU$dBTCTA$dUKMGB$dOHX$dYDXCP$dBWX
041 1 $aeng$hrus
042 $apcc
050 4 $aQA614.83$b.B46 2011
100 1 $aBenenti, Sergio.
245 10 $aHamiltonian structures and generating families /$cSergio Benenti.
260 $aNew York :$bSpringer,$cc2011.
300 $axiv, 258 p. :$bill. ;$c24 cm.
504 $aIncludes bibliographical references (p. 247-251) and index.
500 $a"This book is an enhanced version of an earlier Russian edition"--P. [4] of cover.
546 $aTranslated into English from the original Russian.
505 0 $aPreface.- Basic Notions of Calculus on Manifolds.- Relations.- Symplectic Relations on Symplectic Manifolds.- Symplectic Relations on Cotangent Bundles.- Canonical Lift on Cotangent Bundles.-The Geometry of the Hamilton-Jacobi Equation.- Hamiltonian Optics in Euclidean Spaces.- Control of Static Systems.- Supplementary Topics.- Global Hamilton Principal Functions on S2 and H2 -- References -- Index.
520 $aThis book is an enhanced version of an earlier Russian edition. Besides thorough revisions, more emphasis was put on reordering the topics according to a category-theoretical view. This allows the mathematical results to be stated, proved, and understood in a much easier and elegant way. From the reviews of the Russian edition: "The main accent is shifted to the application . . . in geometrical optics, thermostatics and control theory, and not to the Hamiltonian mechanics only. . . . To make the book fairly self-contained, full details of basic definitions and all proofs are included. In this way, the majority of the text can be read without the prerequisite of a course in geometry. The excellent collection of examples illustrates the relatively hard and highly abstract mathematical theory and its hidden difficulties. . . . The book can rise real interest for specialists . . . .  The . . . book is a significant input in the modern symplectic geometry and its applications." (Andrey Tsiganov, St. Petersburg State University) Sergio Benenti is a professor of mathematical physics at Università di Torino, Italy. His current fields of research include symplectic geometry with applications to physical theories, Riemannian geometry with applications to the theory of the separation of variables in the Hamilton-Jacobi equation and in other relevant differential equations of physics, and mathematical models of the dynamics of non-holonomic systems.
650 0 $aHamiltonian systems.
650 0 $aSymplectic geometry.
650 0 $aSymplectic manifolds.
650 0 $aGlobal analysis.
650 0 $aGlobal differential geometry.
650 0 $aMathematics.
650 0 $aSystems theory.
830 0 $aUniversitext.
988 $a20111213
049 $aCLSL
906 $0OCLC