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001			295527
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008			150903s2006 gw | o |||| 0|eng d
020			_a9783540329022 _99783540329022
024	7		_a10.1007/9783540329022 _2doi
035			_avtls000348538
039		9	_a201509030920 _bVLOAD _c201405050340 _dVLOAD _y201402071030 _zstaff
040			_aMX-SnUAN _bspa _cMX-SnUAN _erda
050		4	_aQA372
100	1		_aDumortier, Freddy. _eautor _9330025
245	1	0	_aQualitative Theory of Planar Differential Systems / _cby Freddy Dumortier, Jaume Llibre, Joan C. Artés.
264		1	_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg, _c2006.
300			_axvI, 302 páginas 123 ilustraciones _brecurso en línea.
336			_atexto _btxt _2rdacontent
337			_acomputadora _bc _2rdamedia
338			_arecurso en línea _bcr _2rdacarrier
347			_aarchivo de texto _bPDF _2rda
500			_aSpringer eBooks
505	0		_aBasic Results on the Qualitative Theory of Differential Equations -- Normal Forms and Elementary Singularities -- Desingularization of Nonelementary Singularities -- Centers and Lyapunov Constants -- Poincaré and Poincaré–Lyapunov Compactification -- Indices of Planar Singular Points -- Limit Cycles and Structural Stability -- Integrability and Algebraic Solutions in Polynomial Vector Fields -- Polynomial Planar Phase Portraits -- Examples for Running P4.
520			_aThe book deals essentially with systems of polynomial autonomous ordinary differential equations in two real variables. The emphasis is mainly qualitative, although attention is also given to more algebraic aspects as a thorough study of the center/focus problem and recent results on integrability. In the last two chapters the performant software tool P4 is introduced: based on both algebraic manipulation and numerical calculation, this was conceived for the purpose of drawing "Polynomial Planar Phase Portraits" on part of the plane, or on a Poincaré compactification, or even on a Poincaré-Lyapunov compactification of the plane. From the start, differential systems are represented by vector fields enabling, in full strength, a dynamical systems approach. All essential notions, including invariant manifolds, normal forms, desingularization of singularities, index theory and limit cycles, are introduced and the main results are proved for smooth systems with the necessary specifications for analytic and polynomial systems. The book is very appropriate for a first course in dynamical systems, presenting the basic notions in the study of individual two dimensional systems. Not only does it provide simple and appropriate proofs, but it also contains a lot of exercises and presents a survey of interesting results with the necessary references to the literature.
590			_aPara consulta fuera de la UANL se requiere clave de acceso remoto.
700	1		_aLlibre, Jaume. _eautor _9325520
700	1		_aArtés, Joan C. _eautor _9330026
710	2		_aSpringerLink (Servicio en línea) _9299170
776	0	8	_iEdición impresa: _z9783540328933
856	4	0	_uhttp://remoto.dgb.uanl.mx/login?url=http://dx.doi.org/10.1007/978-3-540-32902-2 _zConectar a Springer E-Books (Para consulta externa se requiere previa autentificación en Biblioteca Digital UANL)
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999			_c295527 _d295527