Title | Computer Algebra Methods for Equivariant Dynamical Systems [electronic resource] / edited by Karin Gatermann |
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Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 2000 |
Connect to | http://dx.doi.org/10.1007/BFb0104059 |
Descript | XVIII, 162 p. online resource |
Grรถbner bases: Buchberger's algorithm -- The consequence of grading -- Definitions and the relation to Grรถbner bases -- Computation of a Hilbert series -- The Hilbert series driven Buchberger algorithm -- The computation with algebraic extensions -- Detection of Grรถbner bases -- Dynamic Buchberger algorithm -- Elimination -- Algorithms of the computation of invariants and equivariants: Using the Hilbert series -- Invariants -- Equivariants -- Using the nullcone -- Using a homogeneous system of parameters -- Computing uniqueness -- Symmetric bifurcation theory -- Local bifurcation analysis -- An example of secondary Hopf bifurcation -- Orbit space reduction -- Exact computation of steady states -- Differential equations on the orbit space -- Using Noether normalization -- Further reading -- References -- Index