Computer Algebra Methods for Equivariant Dynamical Systems
Springer Berlin (Verlag)
978-3-540-67161-9 (ISBN)
The next chapter describes algorithms in invariant theory including many examples and time tables. These techniques are applied in the chapters on symmetric bifurcation theory and equivariant dynamics.
This combination of different areas of mathematics will be interesting to researchers in computational algebra and/or dynamics.
Gröbner bases: Buchberger's algorithm.- The consequence of grading.- Definitions and the relation to Gröbner bases.- Computation of a Hilbert series.- The Hilbert series driven Buchberger algorithm.- The computation with algebraic extensions.- Detection of Gröbner 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.
| Erscheint lt. Verlag | 27.3.2000 |
|---|---|
| Reihe/Serie | Lecture Notes in Mathematics |
| Zusatzinfo | XVIII, 162 p. |
| Verlagsort | Berlin |
| Sprache | englisch |
| Maße | 156 x 234 mm |
| Gewicht | 238 g |
| Themenwelt | Mathematik / Informatik ► Informatik |
| Mathematik / Informatik ► Mathematik ► Algebra | |
| Schlagworte | Algebra • algorithms • Computer • Computeralgebra • Computer Algebra • Dynamical Systems • Dynamisches System • Dynamische Systeme • Gröbner Bases • Invariant theory • symmetry |
| ISBN-10 | 3-540-67161-7 / 3540671617 |
| ISBN-13 | 978-3-540-67161-9 / 9783540671619 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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