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001 978-3-540-49613-7
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007 cr nn 008mamaa
008 121227s1996 gw | s |||| 0|eng d
020 _a9783540496137
_9978-3-540-49613-7
024 7 _a10.1007/978-3-540-49613-7
_2doi
050 4 _aQA299.6-433
072 7 _aPBK
_2bicssc
072 7 _aMAT034000
_2bisacsh
072 7 _aPBK
_2thema
082 0 4 _a515
_223
100 1 _aBroer, Hendrik W.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aQuasi-Periodic Motions in Families of Dynamical Systems
_h[electronic resource] :
_bOrder amidst Chaos /
_cby Hendrik W. Broer, George B. Huitema, Mikhail B. Sevryuk.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c1996.
300 _aXI, 200 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 ;
_v1645
505 0 _aand examples -- The conjugacy theory -- The continuation theory -- Complicated Whitney-smooth families -- Conclusions -- Appendices.
520 _aThis book is devoted to the phenomenon of quasi-periodic motion in dynamical systems. Such a motion in the phase space densely fills up an invariant torus. This phenomenon is most familiar from Hamiltonian dynamics. Hamiltonian systems are well known for their use in modelling the dynamics related to frictionless mechanics, including the planetary and lunar motions. In this context the general picture appears to be as follows. On the one hand, Hamiltonian systems occur that are in complete order: these are the integrable systems where all motion is confined to invariant tori. On the other hand, systems exist that are entirely chaotic on each energy level. In between we know systems that, being sufficiently small perturbations of integrable ones, exhibit coexistence of order (invariant tori carrying quasi-periodic dynamics) and chaos (the so called stochastic layers). The Kolmogorov-Arnol'd-Moser (KAM) theory on quasi-periodic motions tells us that the occurrence of such motions is open within the class of all Hamiltonian systems: in other words, it is a phenomenon persistent under small Hamiltonian perturbations. Moreover, generally, for any such system the union of quasi-periodic tori in the phase space is a nowhere dense set of positive Lebesgue measure, a so called Cantor family. This fact implies that open classes of Hamiltonian systems exist that are not ergodic. The main aim of the book is to study the changes in this picture when other classes of systems - or contexts - are considered.
650 0 _aGlobal analysis (Mathematics).
650 0 _aDifferentiable dynamical systems.
650 1 4 _aAnalysis.
_0http://scigraph.springernature.com/things/product-market-codes/M12007
650 2 4 _aDynamical Systems and Ergodic Theory.
_0http://scigraph.springernature.com/things/product-market-codes/M1204X
650 2 4 _aTheoretical, Mathematical and Computational Physics.
_0http://scigraph.springernature.com/things/product-market-codes/P19005
700 1 _aHuitema, George B.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
700 1 _aSevryuk, Mikhail B.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783662167953
776 0 8 _iPrinted edition:
_z9783540620259
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1645
856 4 0 _uhttps://doi.org/10.1007/978-3-540-49613-7
912 _aZDB-2-SMA
912 _aZDB-2-LNM
912 _aZDB-2-BAE
999 _c12015
_d12015