UNSPECIFIED (2000) Toric geometry and equivariant bifurcations. PHYSICA D, 143 (1-4). pp. 235-261. ISSN 0167-2789

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Abstract

Many problems in equivariant bifurcation theory involve the computation of invariant functions and equivariant mappings for the action of a torus group. We discuss general methods for finding these based on some elementary considerations related to toric geometry, a powerful technique in algebraic geometry. This approach leads to interesting combinatorial questions about cones in lattices, which lead to explicit calculations of minimal generating sets of invariants, from which the equivariants are easily deduced. We also describe the computation of Hilbert series for torus invariants and equivariants within the same combinatorial framework. As an example, we apply these methods to the interaction of two linear modes of a Euclidean-invariant PDE on a rectangular domain with periodic boundary conditions. (C) 2000 Elsevier Science B.V. All rights reserved.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics Q Science > QC Physics
Journal or Publication Title:	PHYSICA D
Publisher:	ELSEVIER SCIENCE BV
ISSN:	0167-2789
Date:	1 September 2000
Volume:	143
Number:	1-4
Number of Pages:	27
Page Range:	pp. 235-261
Publication Status:	Published
URI:	http://wrap.warwick.ac.uk/id/eprint/13098

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