Hopf Bifurcation with Tetrahedral and Octahedral Symmetry

• Tipo: Artigo em Revista Científica Internacional
• Data: 2016

Autores

Isabel S Labouriau (Autor) FCUP; Murza, AC (Autor) Outra

Revista

Título: SIAM Journal on Applied Dynamical Systems

Vol. 15

Páginas: 125-141

ISSN: 1536-0040

Editora: Society for Industrial and Applied Mathematics

Indexação

ISI Web of Knowledge - 0 Citações

Scopus - 0 Citações

Outras Informações

ID Authenticus: P-00K-DG0

DOI: 10.1137/15m1009317

Abstract (EN): In the study of the periodic solutions of a G-equivariant dynamical system, the H mod K theorem gives all possible periodic solutions, based on group-theoretical aspects. By contrast, the equivariant Hopf theorem guarantees the existence of families of small-amplitude periodic solutions bifurcating from the origin for each C-axial subgroup of Gamma x S-1. In this article we compare the bifurcation of periodic solutions for generic differential equations equivariant under the full group of symmetries of the tetrahedron and the group of rotational symmetries of the cube. The two groups are the image of inequivalent representations of the symmetric group S-4. The possible spatial symmetries of bifurcating solutions are different, even though the two groups yield the same group of matrices Gamma x S-1. The same group of matrices occurs again as the extension Gamma x S-1 when G is the full group of symmetries of the cube. For these three groups, while characterizing the Hopf bifurcation, we identify which periodic solution types, whose existence is guaranteed by the H mod K theorem, are obtainable by Hopf bifurcation from the origin.

Idioma: Inglês

Tipo (Avaliação Docente): Científica

Nº de páginas: 17