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- catalog abstract "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, Gröbner basis techniques, are applied. The readership addressed consists of advanced graduate students and researchers in dynamical systems.".
- catalog contributor b12810040.
- catalog created "c2003.".
- catalog date "2003".
- catalog date "c2003.".
- catalog dateCopyrighted "c2003.".
- catalog description "Includes bibliographical references (p. [159]-165) and index.".
- catalog description "Introduction -- I. Applications: Methods I: Planar reduction; Method II: The energy-momentum map -- II. Theory: Birkhoff Normalization; Singularity Theory; Gröbner bases and Standard bases; Computing normalizing transformations -- Appendix A.1. Classification of term orders; Appendix A.2. Proof of Proposition 5.8 -- References -- Index.".
- catalog description "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, Gröbner basis techniques, are applied. The readership addressed consists of advanced graduate students and researchers in dynamical systems.".
- catalog extent "xiii, 169 p. :".
- catalog hasFormat "Also available in an electronic version.".
- catalog identifier "3540004033 (pbk. : acid-free paper)".
- catalog isFormatOf "Also available in an electronic version.".
- catalog isPartOf "Lecture notes in mathematics (Springer-Verlag) ; 1806.".
- catalog isPartOf "Lecture notes in mathematics, 0075-8434 ; 1806".
- catalog issued "2003".
- catalog issued "c2003.".
- catalog language "eng".
- catalog publisher "Berlin ; New York : Springer-Verlag,".
- catalog relation "Also available in an electronic version.".
- catalog subject "510 s 514/.74 21".
- catalog subject "Bifurcation theory.".
- catalog subject "Computer science.".
- catalog subject "Global analysis (Mathematics)".
- catalog subject "Gröbner bases.".
- catalog subject "Hamiltonian systems.".
- catalog subject "Mathematics.".
- catalog subject "QA3 .L28 no. 1806 QA614.83".
- catalog subject "Singularities (Mathematics)".
- catalog tableOfContents "Introduction -- I. Applications: Methods I: Planar reduction; Method II: The energy-momentum map -- II. Theory: Birkhoff Normalization; Singularity Theory; Gröbner bases and Standard bases; Computing normalizing transformations -- Appendix A.1. Classification of term orders; Appendix A.2. Proof of Proposition 5.8 -- References -- Index.".
- catalog title "Bifurcations in Hamiltonian systems : computing singularities by Gröbner bases / Henk Broer ... [et al.].".
- catalog type "Computer network resources. local".
- catalog type "Electronic books. lcsh".
- catalog type "text".