cx r22 2 45 208010386 http://www.idref.fr/208010386 20171021 20260307015408.000 0499 0499 Tr2 20171021afrey50 ba0 eng 639-2 2003 k fre 0 # # AFNOR Oeuvre Textuelle ba0yba0 Bifurcations in Hamiltonian Systems, Computing Singularities by Gröbner Bases ba0yba0y 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. ba0yba0 Bifurcations in Hamiltonian Systems 190230037 ba0yba05 Hoveijn Igor 19..-.... 070 147295521 ba0yba05 Vegter Gert mathématicien 070 19023024X ba0yba05 Lunter Gerton 19..-.... 070 034055568 ba0yba05 Broer Hendrik Wolter 1950-.... mathématicien 070 Mathematics lc Global analysis lc Computer science lc 02723875X Mathématiques rameau 031498949 Informatique Mathématiques rameau 02739087X Analyse globale (mathématiques) rameau 027296504 Singularités (mathématiques) rameau 033344299 Bases de Gröbner rameau 027492931 Systèmes hamiltoniens rameau 028631560 Théorie de la bifurcation rameau Mathematics Global Analysis and Analysis on Manifolds Computational Science and Engineering FR Abes 20260307 AFNOR