Descripción del título
Qualitative theory of plana...
The 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
Monografía
monografia Rebiun25755726 https://catalogo.rebiun.org/rebiun/record/Rebiun25755726 m o d cr |n||||||||| 060324s2006 gw a ob 001 0 eng c 262692694 316695980 401442811 607266586 613491035 646748770 690012762 739129082 756424345 815640337 816984209 846619253 880110340 985033737 988836684 990615590 990660380 1001351484 1005750121 1011937533 1022047096 1035660479 1040685817 1044190373 1056354136 1058527898 1060665773 1060851041 1066588652 1071909912 1073042778 1077263736 1086931990 1087341952 1089425283 1097090259 1097351276 1097858256 1105599253 1110839682 1110938090 1112534518 1132416100 9783540328933 pbk.) 3540328939 pbk.) 9783540329022 ebook) 3540329021 ebook) 9786611350932 6611350934 9783540329021 10.1007/978-3-540-32902-2 doi AU@ 000042135485 DEBSZ 449602117 DKDLA 820120-katalog:000662654 GBVCP 524925860 NLGGC 38420452X NZ1 12054258 11371328 978-3-540-32893-3 Springer http://www.springerlink.com COO eng pn COO HNK GW5XE UAB OCLCQ MNU E7B UBC YNG OCLCO OCLCQ A7U OCLCQ OCLCF OCLCE SLY YDXCP IDEBK NUI DKDLA EBLCP DEBSZ OCLCQ VT2 Z5A LIP OCLCO OCLCQ STF OCLCQ CEF U3W OCLCQ WYU ICG UWO YOU OCLCQ W2U CNTRU OCLCQ AU@ AUD DCT ZHM OCLCQ ERF OCLCQ pcc dlr QA lcco PBKJ bicssc MAT007000 bisacsh 515/.35 22 31.44 bcl O241. 8 clc SK 520 rvk 510 sdnb MAT 343f stub Dumortier, Freddy Qualitative theory of planar differential systems Freddy Dumortier, Jaume Llibre, Joan C. Artés Berlin New York Springer 2006 Berlin New York Berlin New York Springer 1 online resource (xvi, 298 pages) illustrations 1 online resource (xvi, 298 pages) Text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Universitext Includes bibliographical references (pages 285-293) and index Basic Results on the Qualitative Theory of Differential Equations -- Normal Forms and Elementary Singularities -- Desingularization of Non-elementary Singularities. Centers and Lyapunov Constants. -- Poincaré and Poincaré-Lyapunov Compactification -- Indices of Planar Singular Points -- Limit Cycles and Structural Stability -- Integrability and Algebaric Solutions in Polynomial Vector Fields -- Polynomial Planar Phase Portraits -- Examples for Running P4. -- Bibliography Use copy. Restrictions unspecified star. MiAaHDL The 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 Electronic reproduction. [Place of publication not identified] HathiTrust Digital Library 2011. MiAaHDL Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. http://purl.oclc.org/DLF/benchrepro0212 MiAaHDL English digitized 2011 HathiTrust Digital Library committed to preserve pda MiAaHDL Differential equations- Qualitative theory Differential equations- Numerical solutions Équations différentielles- Théorie qualitative Équations différentielles- Solutions numériques Artés, Joan C. Differential equations- Numerical solutions. Teoria qualitativa. Equações diferenciais ordinárias (textos avançados) Équations différentielles- Théorie qualitative. Équations différentielles- Solutions numériques. Artés, Joan C. Differential equations- Qualitative theory. Differential equations- Numerical solutions. Differential equations- Qualitative theory. Qualitative Theorie. System von gewöhnlichen Differentialgleichungen. Teoria qualitativa. Equações diferenciais ordinárias (textos avançados) Electronic books Llibre, Jaume Artés, Joan C. 1961-) Springer e-books Springer e-books Print version Dumortier, Freddy. Qualitative theory of planar differential systems. Berlin ; New York : Springer, 2006 9783540328933 3540328939 (DLC) 2006924563 (OCoLC)71336250 Online version Dumortier, Freddy. Qualitative theory of planar differential systems. Berlin ; New York : Springer, 2006 (OCoLC)816984209 Universitext