Computer Algebra Methods for Equivariant Dynamical Systems

• Κύριος συγγραφέας: Gatermann, Karin (Συγγραφέας, http://id.loc.gov/vocabulary/relators/aut)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2000.
• Έκδοση: 1st ed. 2000.
• Σειρά: Lecture Notes in Mathematics, 1728
• Θέματα: Algebra.; Computer science-Mathematics.; Computer mathematics.; Mathematical analysis.; Analysis (Mathematics).; Global analysis (Mathematics).; Manifolds (Mathematics).; Mathematics of Computing.; Computational Science and Engineering.; Math Applications in Computer Science.; Analysis.; Global Analysis and Analysis on Manifolds.

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 table...

Πίνακας περιεχομένων:

• 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.