Tomoaki Chiba and Hiroyuki Nagahama
Institute of Geology and Paleontology, Graduate School of Science, Tohoku University, Sendai 980-8578, Japan
(Received September 14, 2001; Accepted October 22, 2001)
Keywords: Curie Principle, Symmetry Breaking, Nonlinear Systems, Group Theory, Functional Analysis
Abstract. The Curie symmetry principle states that the effect may occasionally have the same or a higher symmetry than the causes. But breaking this principle occurs in some nonlinear phenomena such as buckling of a cylinder. Sattinger's group theoretical method mathematically explains that these phenomena dominated by nonlinear functional equations break the Curie principle. The result of the group theoretical method manifests that both cases preserving and breaking the Curie principle occur in the same nonlinear system.