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
Resource Information
The item Qualitative theory of planar differential systems, Freddy Dumortier, Jaume Llibre, Joan C. Artés represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item Qualitative theory of planar differential systems, Freddy Dumortier, Jaume Llibre, Joan C. Artés represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.
This item is available to borrow from 1 library branch.
- 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
- 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
- Label
- Qualitative theory of planar differential systems
- Title
- Qualitative theory of planar differential systems
- Statement of responsibility
- Freddy Dumortier, Jaume Llibre, Joan C. Artés
- Subject
-
- Artés, Joan C
- Differential equations -- Numerical solutions
- Differential equations -- Numerical solutions
- Differential equations -- Numerical solutions
- Differential equations -- Numerical solutions
- Differential equations -- Qualitative theory
- Differential equations -- Qualitative theory
- Differential equations -- Qualitative theory
- Differential equations -- Qualitative theory
- Equações diferenciais ordinárias (textos avançados)
- Equações diferenciais ordinárias (textos avançados)
- Qualitative Theorie
- System von gewöhnlichen Differentialgleichungen
- Teoria qualitativa
- Teoria qualitativa
- Équations différentielles -- Solutions numériques
- Équations différentielles -- Solutions numériques
- Équations différentielles -- Théorie qualitative
- Équations différentielles -- Théorie qualitative
- Artés, Joan C
- 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
- 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
- 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
- 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
- Artés, Joan C
- Differential equations -- Numerical solutions
- Differential equations -- Numerical solutions
- Differential equations -- Numerical solutions
- Differential equations -- Numerical solutions
- Differential equations -- Qualitative theory
- Differential equations -- Qualitative theory
- Differential equations -- Qualitative theory
- Differential equations -- Qualitative theory
- Equações diferenciais ordinárias (textos avançados)
- Equações diferenciais ordinárias (textos avançados)
- Qualitative Theorie
- System von gewöhnlichen Differentialgleichungen
- Teoria qualitativa
- Teoria qualitativa
- Équations différentielles -- Solutions numériques
- Équations différentielles -- Solutions numériques
- Équations différentielles -- Théorie qualitative
- Équations différentielles -- Théorie qualitative
- Artés, Joan C
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<div class="citation" vocab="http://schema.org/"><i class="fa fa-external-link-square fa-fw"></i> Data from <span resource="http://link.library.missouri.edu/portal/Qualitative-theory-of-planar-differential/jljTcerBLQ0/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.missouri.edu/portal/Qualitative-theory-of-planar-differential/jljTcerBLQ0/">Qualitative theory of planar differential systems, Freddy Dumortier, Jaume Llibre, Joan C. Artés</a></span> - <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.missouri.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.missouri.edu/">University of Missouri Libraries</a></span></span></span></span></div>