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020 _a9783540315506
_9978-3-540-31550-6
024 7 _a10.1007/b105138
_2doi
050 4 _aQC19.2-20.85
072 7 _aPHU
_2bicssc
072 7 _aSCI040000
_2bisacsh
072 7 _aPHU
_2thema
082 0 4 _a530.1
_223
100 1 _aEfstathiou, Konstantinos.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aMetamorphoses of Hamiltonian Systems with Symmetries
_h[electronic resource] /
_cby Konstantinos Efstathiou.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2005.
300 _aIX, 149 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1864
505 0 _aIntroduction -- 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.
520 _aModern 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.
650 0 _aDifferentiable dynamical systems.
650 0 _aTopological Groups.
650 0 _aStatistical physics.
650 1 4 _aTheoretical, Mathematical and Computational Physics.
_0http://scigraph.springernature.com/things/product-market-codes/P19005
650 2 4 _aComplex Systems.
_0http://scigraph.springernature.com/things/product-market-codes/P33000
650 2 4 _aDynamical Systems and Ergodic Theory.
_0http://scigraph.springernature.com/things/product-market-codes/M1204X
650 2 4 _aTopological Groups, Lie Groups.
_0http://scigraph.springernature.com/things/product-market-codes/M11132
650 2 4 _aStatistical Physics and Dynamical Systems.
_0http://scigraph.springernature.com/things/product-market-codes/P19090
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783540806813
776 0 8 _iPrinted edition:
_z9783540243168
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1864
856 4 0 _uhttps://doi.org/10.1007/b105138
912 _aZDB-2-SMA
912 _aZDB-2-LNM
999 _c9879
_d9879