Bifurcations in Hamiltonian systems
Subtitle: computing singularities by Gröbner bases
By: Henk Broer ... [et al.].
Contributors: Broer, H. W. 1950-
Series: Lecture notes in mathematics -- 1806.; Lecture notes in mathematics (Springer-Verlag) -- 1806.
Publisher: Springer-Verlag
Published: 2003
Place of publication: New York
Language: eng
Number of pages: 169
Subjects: Hamiltonian systems; Bifurcation theory; Singularities (Mathematics); Gröbner bases
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.
Notes: Includes bibliographical references and index.