GENERATING FUNCTIONS FOR HOPF BIFURCATION WITH S-n-SYMMETRY

• Type: Article in International Scientific Journal
• Date: 2009

Authors

dias, aps (Author) FCUP; matthews, pc (Author) Other; rodrigues, a (Author) Other

Journal

Title: Discrete and Continuous Dynamical Systems

Vol. 25 No. 3

Pages: 823-842

ISSN: 1078-0947

Publisher: American Institute of Mathematical Sciences

Indexing

ISI Web of Knowledge - 1 Citation

Scopus - 1 Citation

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-003-EJ7

DOI: 10.3934/dcds.2009.25.823

Abstract (EN): Hopf bifurcation in the presence of the symmetric group S-n (acting naturally by permutation of coordinates) is a problem with relevance to coupled oscillatory systems. To study this bifurcation it is important to construct the Taylor expansion of the equivariant vector field in normal form. We derive generating functions for the numbers of linearly independent invariants and equivariants of any degree, and obtain recurrence relations for these functions. This enables us to determine the number of invariants and equivariants for all n, and show that this number is independent of n for sufficiently large n. We also explicitly construct the equivariants of degree three and degree five, which are valid for arbitrary n.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 20