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The Resource Bifurcations in Hamiltonian systems : computing singularities by Gröbner bases, Henk Broer [and others]

Bifurcations in Hamiltonian systems : computing singularities by Gröbner bases, Henk Broer [and others]

Contributor
Summary
The authors consider applications of singularity theory and computer algebra to bifurcations of Hamiltonian dynamical systems. They restrict themselves to the case were the following simplification is possible. Near the equilibrium or (quasi- ) periodic solution under consideration the linear part allows approximation by a normalized Hamiltonian system with a torus symmetry. It is assumed that reduction by this symmetry leads to a system with one degree of freedom. The volume focuses on two such reduction methods, the planar reduction (or polar coordinates) method and the reduction by the energy momentum mapping. The one-degree-of-freedom system then is tackled by singularity theory, where computer algebra, in particular, Grbner basis techniques, are applied. The readership addressed consists of advanced graduate students and researchers in dynamical systems
Language
eng
Work
Publication
Extent
1 online resource (xiii, 169 pages)
Contents
  • Introduction
  • I. Applications: Methods I: Planar reduction; Method II: The energy-momentum map
  • II. Theory: Birkhoff Normalization; Singularity Theory; Grbner bases and Standard bases; Computing normalizing transformations
  • Appendix A.1. Classification of term orders; Appendix A.2. Proof of Proposition 5.8
  • References
  • Index
Isbn
9783540363989
Instance
Label
Bifurcations in Hamiltonian systems : computing singularities by Gröbner bases
Title
Bifurcations in Hamiltonian systems
Title remainder
computing singularities by Gröbner bases
Statement of responsibility
Henk Broer [and others]
Contributor
Subject
Language
eng
Summary
The authors consider applications of singularity theory and computer algebra to bifurcations of Hamiltonian dynamical systems. They restrict themselves to the case were the following simplification is possible. Near the equilibrium or (quasi- ) periodic solution under consideration the linear part allows approximation by a normalized Hamiltonian system with a torus symmetry. It is assumed that reduction by this symmetry leads to a system with one degree of freedom. The volume focuses on two such reduction methods, the planar reduction (or polar coordinates) method and the reduction by the energy momentum mapping. The one-degree-of-freedom system then is tackled by singularity theory, where computer algebra, in particular, Grbner basis techniques, are applied. The readership addressed consists of advanced graduate students and researchers in dynamical systems
Member of
Cataloging source
COO
Dewey number
  • 510 s
  • 514/.74
Illustrations
illustrations
Index
index present
LC call number
  • QA3
  • QA614.83
LC item number
.L28 no. 1806
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorDate
1950-
http://library.link/vocab/relatedWorkOrContributorName
Broer, H. W.
Series statement
Lecture notes in mathematics,
Series volume
1806
http://library.link/vocab/subjectName
  • Hamiltonian systems
  • Bifurcation theory
  • Singularities (Mathematics)
  • Gröbner bases
  • Bifurcation theory
  • Gröbner bases
  • Hamiltonian systems
  • Singularities (Mathematics)
Label
Bifurcations in Hamiltonian systems : computing singularities by Gröbner bases, Henk Broer [and others]
Instantiates
Publication
Bibliography note
Includes bibliographical references (pages 159-165) 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
Introduction -- I. Applications: Methods I: Planar reduction; Method II: The energy-momentum map -- II. Theory: Birkhoff Normalization; Singularity Theory; Grbner bases and Standard bases; Computing normalizing transformations -- Appendix A.1. Classification of term orders; Appendix A.2. Proof of Proposition 5.8 -- References -- Index
Control code
51944878
Dimensions
unknown
Extent
1 online resource (xiii, 169 pages)
Form of item
online
Isbn
9783540363989
Lccn
2003041220
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other physical details
illustrations.
Specific material designation
remote
System control number
(OCoLC)51944878
Label
Bifurcations in Hamiltonian systems : computing singularities by Gröbner bases, Henk Broer [and others]
Publication
Bibliography note
Includes bibliographical references (pages 159-165) 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
Introduction -- I. Applications: Methods I: Planar reduction; Method II: The energy-momentum map -- II. Theory: Birkhoff Normalization; Singularity Theory; Grbner bases and Standard bases; Computing normalizing transformations -- Appendix A.1. Classification of term orders; Appendix A.2. Proof of Proposition 5.8 -- References -- Index
Control code
51944878
Dimensions
unknown
Extent
1 online resource (xiii, 169 pages)
Form of item
online
Isbn
9783540363989
Lccn
2003041220
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other physical details
illustrations.
Specific material designation
remote
System control number
(OCoLC)51944878

Subject

Member of

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