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MARC 21

Computer Algebra Methods for Equivariant Dynamical Systems
Tag	Description
020	$a9783540465195$9978-3-540-46519-5
082	$a512$223
099	$aOnline resource: Springer
245	$aComputer Algebra Methods for Equivariant Dynamical Systems$h[EBook] /$cedited by Karin Gatermann.
260	$aBerlin, Heidelberg :$bSpringer Berlin Heidelberg :$bImprint: Springer,$c2000.
300	$aXVIII, 162 p.$bonline resource.
336	$atext$btxt$2rdacontent
337	$acomputer$bc$2rdamedia
338	$aonline resource$bcr$2rdacarrier
440	$aLecture Notes in Mathematics,$x0075-8434 ;$v1728
505	$aGröbner 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.
520	$aThis 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.
538	$aOnline access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
700	$aGatermann, Karin.$eeditor.
710	$aSpringerLink (Online service)
830	$aLecture Notes in Mathematics,$x0075-8434 ;$v1728
856	$uhttp://dx.doi.org/10.1007/BFb0104059