Bifurcations in Hamiltonian systems: computing singularities by Gröbner bases / Henk Broer, Igor Hoveijn, Gerton Lunter ... [et al.]

Auteur: Broer, Hendrik Wolter (1950-) - AuteurCo-auteur: Lunter, Gerton - Auteur ; Hoveijn, Igor (1959-) - AuteurType de document: Livre numériqueCollection: Lecture notes in mathematics, (Online) ; 1806Langue: anglaisÉditeur: Berlin : Springer, 2003 ISBN: 9783540004035 ISSN: 1617-9692Note: “This book deals with nonlinear Hamiltonian systems, depending on parameters.... The general goal is to understand their dynamics in a qualitative, and if possible, also quantitative way. In many important cases, it is possible to reduce a skeleton of the dynamics to lower dimension, sometimes leading to a Hamiltonian system in one degree of freedom. Such reduced systems allow a singularity theory or catastrophe theory approach which gives raise to transparent, in a sense polynomial, normal forms. Moreover the whole process of arriving at these normal forms is algorithmic. The purpose of this book is to develop computer-algebraic tools for the implementation of these algorithms. This set-up allows for many applications concerning resonances in coupled or driven oscillators, the n-body problem, the dynamics of the rigid body ...”. This description opens the book, and conveniently summarizes its scope. ... (Zentralblatt) Sujets MSC: 37J15 Dynamical systems and ergodic theory -- Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems -- Symmetries, invariants, invariant manifolds, momentum maps, reduction
37G05 Dynamical systems and ergodic theory -- Local and nonlocal bifurcation theory -- Normal forms
37J20 Dynamical systems and ergodic theory -- Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems -- Bifurcation problems
58Kxx Global analysis, analysis on manifolds -- Theory of singularities and catastrophe theory
37M20 Dynamical systems and ergodic theory -- Approximation methods and numerical treatment of dynamical systems -- Computational methods for bifurcation problems
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“This book deals with nonlinear Hamiltonian systems, depending on parameters....

The general goal is to understand their dynamics in a qualitative, and if possible, also quantitative way. In many important cases, it is possible to reduce a skeleton of the dynamics to lower dimension, sometimes leading to a Hamiltonian system in one degree of freedom. Such reduced systems allow a singularity theory or catastrophe theory approach which gives raise to transparent, in a sense polynomial, normal forms. Moreover the whole process of arriving at these normal forms is algorithmic. The purpose of this book is to develop computer-algebraic tools for the implementation of these algorithms. This set-up allows for many applications concerning resonances in coupled or driven oscillators, the n-body problem, the dynamics of the rigid body ...”. This description opens the book, and conveniently summarizes its scope. ... (Zentralblatt)

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