Forma, Vol. 16 (No. 3), pp. 225-231, 2001
Original Paper

Curie Symmetry Principle in Nonlinear Functional Systems

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.

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