Applications of equivariant degree for gradient maps to symmetric Newtonian systems
2007; Elsevier BV; Volume: 68; Issue: 6 Linguagem: Inglês
10.1016/j.na.2006.12.039
ISSN1873-5215
Autores Tópico(s)Nonlinear Partial Differential Equations
ResumoWe consider G=Γ×S1 with Γ being a finite group, for which the complete Euler ring structure in U(G) is described. The multiplication tables for Γ=D6, S4 and A5 are provided in the Appendix. The equivariant degree for G-orthogonal maps is constructed using the primary equivariant degree with one free parameter. We show that the G-orthogonal degree extends the degree for G-gradient maps (in the case of G=Γ×S1) introduced by Gȩba in [K. Gȩba, W. Krawcewicz, J. Wu, An equivariant degree with applications to symmetric bifurcation problems I: Construction of the degree, Bull. London. Math. Soc. 69 (1994) 377–398]. The computational results obtained are applied to a Γ-symmetric autonomous Newtonian system for which we study the existence of 2π-periodic solutions. For some concrete cases, we present the symmetric classification of the solution set for the systems considered.
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