Borrow it
Coverart for item
The Resource Qualitative theory of planar differential systems, Freddy Dumortier, Jaume Llibre, Joan C. Artés

Qualitative theory of planar differential systems, Freddy Dumortier, Jaume Llibre, Joan C. Artés

Creator
Contributor
Summary
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
Language
eng
Work
Publication
Extent
1 online resource (xvi, 298 pages)
Contents
  • 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
Isbn
9786611350932
Instance
Label
Qualitative theory of planar differential systems
Title
Qualitative theory of planar differential systems
Statement of responsibility
Freddy Dumortier, Jaume Llibre, Joan C. Artés
Creator
Contributor
Subject
Language
eng
Summary
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
Member of
Is part of
Action
digitized
Cataloging source
COO
http://library.link/vocab/creatorName
Dumortier, Freddy
Dewey number
515/.35
Illustrations
illustrations
Index
index present
Language note
English
LC call number
QA372
LC item number
.D84 2006
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorDate
1961-
http://library.link/vocab/relatedWorkOrContributorName
  • Llibre, Jaume
  • Artés, Joan C.
Series statement
Universitext
http://library.link/vocab/subjectName
  • Differential equations
  • Differential equations
  • Équations différentielles
  • Équations différentielles
  • Artés, Joan C
  • Differential equations
  • Teoria qualitativa
  • Equações diferenciais ordinárias (textos avançados)
  • Équations différentielles
  • Équations différentielles
  • Artés, Joan C
  • Differential equations
  • Differential equations
  • Differential equations
  • Qualitative Theorie
  • System von gewöhnlichen Differentialgleichungen
  • Teoria qualitativa
  • Equações diferenciais ordinárias (textos avançados)
Label
Qualitative theory of planar differential systems, Freddy Dumortier, Jaume Llibre, Joan C. Artés
Instantiates
Publication
Bibliography note
Includes bibliographical references (pages 285-293) and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
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
Control code
185038304
Dimensions
unknown
Extent
1 online resource (xvi, 298 pages)
Form of item
online
Isbn
9786611350932
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-540-32902-2
Other physical details
illustrations.
http://library.link/vocab/ext/overdrive/overdriveId
978-3-540-32893-3
Publisher number
11371328
Reproduction note
Electronic reproduction.
Specific material designation
remote
System control number
(OCoLC)185038304
System details
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.
Label
Qualitative theory of planar differential systems, Freddy Dumortier, Jaume Llibre, Joan C. Artés
Publication
Bibliography note
Includes bibliographical references (pages 285-293) and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
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
Control code
185038304
Dimensions
unknown
Extent
1 online resource (xvi, 298 pages)
Form of item
online
Isbn
9786611350932
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-540-32902-2
Other physical details
illustrations.
http://library.link/vocab/ext/overdrive/overdriveId
978-3-540-32893-3
Publisher number
11371328
Reproduction note
Electronic reproduction.
Specific material designation
remote
System control number
(OCoLC)185038304
System details
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.

Subject

Member of

Library Locations

    • Ellis LibraryBorrow it
      1020 Lowry Street, Columbia, MO, 65201, US
      38.944491 -92.326012

Library Links

Structured data from the Bibframe namespace is licensed under the Creative Commons Attribution 4.0 International License by University of Missouri Libraries. Additional terms may apply to data associated with third party namespaces.
Processing Feedback ...