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

“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)