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- W2067076295 abstract "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 constructthe Taylor expansion of the equivariant vector field in normal form.We derive generating functions for the numbers of linearlyindependent invariants and equivariants of any degree, and obtainrecurrence relationsfor these functions. This enables us to determine the numberof invariants and equivariants for all $n$, and show that this numberis independent of $n$ for sufficiently large $n$.We also explicitly construct the equivariants of degree threeand degree five, which are valid for arbitrary $n$." @default.
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- W2067076295 date "2009-01-01" @default.
- W2067076295 modified "2023-09-25" @default.
- W2067076295 title "Generating functions for Hopf bifurcation with $ S_n$-symmetry" @default.
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- W2067076295 doi "https://doi.org/10.3934/dcds.2009.25.823" @default.
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