LEADER 05758nam 22008055 450 001 9910300425003321 005 20200702140119.0 010 $a94-017-9220-8 024 7 $a10.1007/978-94-017-9220-2 035 $a(CKB)3710000000249143 035 $a(EBL)1966722 035 $a(OCoLC)892396012 035 $a(SSID)ssj0001354141 035 $a(PQKBManifestationID)11732957 035 $a(PQKBTitleCode)TC0001354141 035 $a(PQKBWorkID)11322533 035 $a(PQKB)10112462 035 $a(DE-He213)978-94-017-9220-2 035 $a(MiAaPQ)EBC1966722 035 $a(PPN)181347814 035 $a(EXLCZ)993710000000249143 100 $a20140923d2015 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aGeometry from Dynamics, Classical and Quantum /$fby José F. Cariñena, Alberto Ibort, Giuseppe Marmo, Giuseppe Morandi 205 $a1st ed. 2015. 210 1$aDordrecht :$cSpringer Netherlands :$cImprint: Springer,$d2015. 215 $a1 online resource (739 p.) 300 $aDescription based upon print version of record. 311 $a94-017-9219-4 320 $aIncludes bibliographical references and index. 327 $aContents -- Foreword -- Some examples of linear and nonlinear physical systems and their dynamical equations -- The language of geometry and dynamical systems: the linearity paradigm -- The geometrization of dynamical systems -- Invariant structures for dynamical systems: Poisson and Jacobi dynamics -- The classical formulations of dynamics of Hamilton and Lagrange -- The geometry of Hermitean spaces: quantum evolution -- Folding and unfolding Classical and Quantum systems -- Integrable and superintegrable systems -- Lie-Scheffers systems -- Appendices -- Bibliography -- Index. 330 $aThis book describes, by using elementary techniques, how some geometrical structures widely used today in many areas of physics, like symplectic, Poisson, Lagrangian, Hermitian, etc., emerge from dynamics. It is assumed that what can be accessed in actual experiences when studying a given system is just its dynamical behavior that is described by using a family of variables ("observables" of the system). The book departs from the principle that ''dynamics is first'', and then tries to answer in what sense the sole dynamics determines the geometrical structures that have proved so useful to describe the dynamics in so many important instances. In this vein it is shown that most of the geometrical structures that are used in the standard presentations of classical dynamics (Jacobi, Poisson, symplectic, Hamiltonian, Lagrangian) are determined, though in general not uniquely, by the dynamics alone. The same program is accomplished for the geometrical structures relevant to describe quantum dynamics. Finally, it is shown that further properties that allow the explicit description of the dynamics of certain dynamical systems, like integrability and superintegrability, are deeply related to the previous development and will be covered in the last part of the book. The mathematical framework used to present the previous program is kept to an elementary level throughout the text, indicating where more advanced notions will be needed to proceed further. A family of relevant examples is discussed at length and the necessary ideas from geometry are elaborated along the text. However no effort is made to present an ''all-inclusive'' introduction to differential geometry as many other books already exist on the market doing exactly that. However, the development of the previous program, considered as the posing and solution of a generalized inverse problem for geometry, leads to new ways of thinking and relating some of the most conspicuous geometrical structures appearing in Mathematical and Theoretical Physics. 606 $aMathematical physics 606 $aStatistical physics 606 $aDynamics 606 $aGeometry, Differential 606 $aMechanics 606 $aTheoretical, Mathematical and Computational Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19005 606 $aMathematical Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/M35000 606 $aComplex Systems$3https://scigraph.springernature.com/ontologies/product-market-codes/P33000 606 $aDifferential Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21022 606 $aClassical Mechanics$3https://scigraph.springernature.com/ontologies/product-market-codes/P21018 606 $aStatistical Physics and Dynamical Systems$3https://scigraph.springernature.com/ontologies/product-market-codes/P19090 615 0$aMathematical physics. 615 0$aStatistical physics. 615 0$aDynamics. 615 0$aGeometry, Differential. 615 0$aMechanics. 615 14$aTheoretical, Mathematical and Computational Physics. 615 24$aMathematical Physics. 615 24$aComplex Systems. 615 24$aDifferential Geometry. 615 24$aClassical Mechanics. 615 24$aStatistical Physics and Dynamical Systems. 676 $a516.36 676 $a530 676 $a530.1 676 $a530.15 700 $aCariñena$b José F$4aut$4http://id.loc.gov/vocabulary/relators/aut$01062987 702 $aIbort$b Alberto$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aMarmo$b Giuseppe$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aMorandi$b Giuseppe$4aut$4http://id.loc.gov/vocabulary/relators/aut 906 $aBOOK 912 $a9910300425003321 996 $aGeometry from Dynamics, Classical and Quantum$92529464 997 $aUNINA