04292nam 22008775 450 99646648130331620200705114651.03-540-31550-010.1007/b105138(CKB)1000000000231927(DE-He213)978-3-540-31550-6(SSID)ssj0000318909(PQKBManifestationID)11242009(PQKBTitleCode)TC0000318909(PQKBWorkID)10336372(PQKB)10219958(MiAaPQ)EBC6283819(MiAaPQ)EBC4976017(MiAaPQ)EBC5578625(Au-PeEL)EBL4976017(CaONFJC)MIL140222(OCoLC)1024264248(Au-PeEL)EBL5578625(OCoLC)262677875(PPN)123091152(EXLCZ)99100000000023192720100806d2005 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierMetamorphoses of Hamiltonian Systems with Symmetries[electronic resource] /by Konstantinos Efstathiou1st ed. 2005.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,2005.1 online resource (IX, 149 p.) Lecture Notes in Mathematics,0075-8434 ;1864Bibliographic Level Mode of Issuance: Monograph3-540-24316-X Includes bibliographical references and index.Introduction -- Four Hamiltonian Systems -- Small Vibrations of Tetrahedral Molecules -- The Hydrogen Atom in Crossed Fields -- Quadratic Spherical Pendula -- Fractional Monodromy in the 1: - 2 Resonance System -- The Tetrahedral Group -- Local Properties of Equilibria -- References -- Index.Modern notions and important tools of classical mechanics are used in the study of concrete examples that model physically significant molecular and atomic systems. The parametric nature of these examples leads naturally to the study of the major qualitative changes of such systems (metamorphoses) as the parameters are varied. The symmetries of these systems, discrete or continuous, exact or approximate, are used to simplify the problem through a number of mathematical tools and techniques like normalization and reduction. The book moves gradually from finding relative equilibria using symmetry, to the Hamiltonian Hopf bifurcation and its relation to monodromy and, finally, to generalizations of monodromy.Lecture Notes in Mathematics,0075-8434 ;1864Mathematical physicsStatistical physicsDynamical systemsDynamicsErgodic theoryTopological groupsLie groupsTheoretical, Mathematical and Computational Physicshttps://scigraph.springernature.com/ontologies/product-market-codes/P19005Complex Systemshttps://scigraph.springernature.com/ontologies/product-market-codes/P33000Dynamical Systems and Ergodic Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M1204XTopological Groups, Lie Groupshttps://scigraph.springernature.com/ontologies/product-market-codes/M11132Statistical Physics and Dynamical Systemshttps://scigraph.springernature.com/ontologies/product-market-codes/P19090Mathematical physics.Statistical physics.Dynamical systems.Dynamics.Ergodic theory.Topological groups.Lie groups.Theoretical, Mathematical and Computational Physics.Complex Systems.Dynamical Systems and Ergodic Theory.Topological Groups, Lie Groups.Statistical Physics and Dynamical Systems.515.7222Efstathiou Konstantinosauthttp://id.loc.gov/vocabulary/relators/aut472491MiAaPQMiAaPQMiAaPQBOOK996466481303316Metamorphoses of Hamiltonian systems with symmetries230758UNISA