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Computer Algebra Methods for Equivariant Dynamical Systems de Karin Gatermann

Computer Algebra Methods for Equivariant Dynamical Systems: Lecture Notes in Mathematics, cartea 1728

Autor Karin Gatermann
en Limba Engleză Paperback – 27 mar 2000
This book starts with an overview of the research of Gröbner bases which have many applications in various areas of mathematics since they are a general tool for the investigation of polynomial systems.
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.
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Specificații

ISBN-13: 9783540671619
ISBN-10: 3540671617
Pagini: 180
Ilustrații: XVIII, 162 p.
Dimensiuni: 156 x 234 x 9 mm
Greutate: 0.27 kg
Ediția:2000
Editura: Springer Berlin, Heidelberg
Colecția Springer
Seria Lecture Notes in Mathematics

Locul publicării:Berlin, Heidelberg, Germany

Public țintă

Research

Cuprins

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.