000			03046nam a22004335i 4500
001			978-94-6239-021-8
003			DE-He213
005			20140220082947.0
007			cr nn 008mamaa
008			131017s2013 fr | s |||| 0|eng d
020			_a9789462390218 _9978-94-6239-021-8
024	7		_a10.2991/978-94-6239-021-8 _2doi
050		4	_aQA372
072		7	_aPBKJ _2bicssc
072		7	_aMAT007000 _2bisacsh
082	0	4	_a515.352 _223
100	1		_aSideris, Thomas C. _eauthor.
245	1	0	_aOrdinary Differential Equations and Dynamical Systems _h[electronic resource] / _cby Thomas C. Sideris.
264		1	_aParis : _bAtlantis Press : _bImprint: Atlantis Press, _c2013.
300			_aXI, 225 p. 11 illus. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aAtlantis Studies in Differential Equations, _x2214-6253 ; _v2
505	0		_aIntroduction -- Linear Systems -- Existence Theory -- Nonautomous Linear Systems -- Results from Functional Analysis -- Dependence on Initial Conditions and Parameters -- Linearization and Invariant Manifolds -- Periodic Solutions -- Center Manifolds and Bifurcation Theory -- The Birkhoff Smale Homoclinic Theorem -- Appendix: Results from Real Analysis.
520			_aThis book is a mathematically rigorous introduction to the beautiful subject of ordinary differential equations for beginning graduate or advanced undergraduate students. Students should have a solid background in analysis and linear algebra. The presentation emphasizes commonly used techniques without necessarily striving for completeness or for the treatment of a large number of topics. The first half of the book is devoted to the development of the basic theory: linear systems, existence and uniqueness of solutions to the initial value problem, flows, stability, and smooth dependence of solutions upon initial conditions and parameters. Much of this theory also serves as the paradigm for evolutionary partial differential equations. The second half of the book is devoted to geometric theory: topological conjugacy, invariant manifolds, existence and stability of periodic solutions, bifurcations, normal forms, and the existence of transverse homoclinic points and their link to chaotic dynamics. A common thread throughout the second part is the use of the implicit function theorem in Banach space. Chapter 5, devoted to this topic, the serves as the bridge between the two halves of the book.
650		0	_aMathematics.
650		0	_aDifferential Equations.
650	1	4	_aMathematics.
650	2	4	_aOrdinary Differential Equations.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9789462390201
830		0	_aAtlantis Studies in Differential Equations, _x2214-6253 ; _v2
856	4	0	_uhttp://dx.doi.org/10.2991/978-94-6239-021-8
912			_aZDB-2-SMA
999			_c100150 _d100150