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Computer Algebra Methods for Equivariant Dynamical Systems

Computer Algebra Methods for Equivariant Dynamical Systems
Catalogue Information
Field name Details
Dewey Class 512
Title Computer Algebra Methods for Equivariant Dynamical Systems ([EBook] /) / edited by Karin Gatermann.
Added Personal Name Gatermann, Karin editor.
Other name(s) SpringerLink (Online service)
Publication Berlin, Heidelberg : : Springer Berlin Heidelberg : : Imprint: Springer, , 2000.
Physical Details XVIII, 162 p. : online resource.
Series Lecture Notes in Mathematics 0075-8434 ; ; 1728
ISBN 9783540465195
Summary Note 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.:
Contents note 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.
System details note Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site http://dx.doi.org/10.1007/BFb0104059
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