Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5773997 | Journal of Differential Equations | 2017 | 47 Pages |
Abstract
The existence of periodic solutions in Î-symmetric Newtonian systems x¨=ââf(x) can be effectively studied by means of the ÎÃO(2)-equivariant gradient degree with values in the Euler ring U(ÎÃO(2)). In this paper we show that in the case of Î being a finite group, the Euler ring U(ÎÃO(2)) and the related basic degrees are effectively computable using Euler ring homomorphisms, the Burnside ring A(ÎÃO(2)), and the reduced ÎÃO(2)-degree with no free parameters. We present several examples of Newtonian systems with various symmetries, for which we show existence of multiple periodic solutions. We also provide exact value of the equivariant topological invariant for those problems.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Mieczyslaw Dabkowski, Wieslaw Krawcewicz, Yanli Lv, Hao-Pin Wu,