imprint:
The Rocky Mountain Mathematics Consortium, 2010
Published in:The Rocky Mountain Journal of Mathematics
Language:
English
ISSN:
0035-7596;
1945-3795
Origination:
Footnote:
Description:
<p>For a finite group Γ, we consider a Γ symmetric autonomous Newtonian system, which is asymptotically linear at ∞ and has 0 and ∞ as isolated degenerate critical points of the corresponding energy function. By means of the equivariant degree theory for gradient G-maps with G = Γ × S¹, we associate to the system a topological invariant deg∞ — deg₀, which is computable up to an unknown factor due to the degeneracy of the system. Under certain assumptions, this invariant still contains enough information about the symmetric structure of the set of periodic solutions, including the existence, multiplicity and symmetric classification. Numerical examples are provided for Γ being the dihedral groups D₆, D₈, D₁₀, D₁₂.</p>