Toric geometry and equivariant bifurcations

• Tipo: Artigo em Revista Científica Internacional
• Data: 2000

Autores

stewart, i (Autor) Outra; dias, aps (Autor) FCUP

Revista

Título: Physica D: Nonlinear Phenomena

Vol. 143

Páginas: 235-261

ISSN: 0167-2789

Editora: Elsevier

Indexação

ISI Web of Knowledge - 1 Citação

Scopus - 1 Citação

Classificação Científica

FOS: Ciências exactas e naturais > Matemática

Outras Informações

ID Authenticus: P-000-Z5S

DOI: 10.1016/s0167-2789(00)00104-4

Abstract (EN): 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.

Idioma: Inglês

Tipo (Avaliação Docente): Científica

Nº de páginas: 27