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In this article we establish the following result: if a nondegenerate quadratic endomorphism of the plane has no fixed points, then every point has empty omega-limit set and alpha-limit set. It is also shown that there exists a six parameter family open and dense in the space of all quadratic mappings of the plane (even those having fixed points). The degenerate case (when the quadratic forms of both components are linearly dependent), for which the theorem fails, is considered in the last section.

In this paper we derive uniqueness, instability and structural stability of solutions in the linear dynamical problem of magneto-elasticity for bounded domains. Section seven is devoted to study spatial decay estimates in the static case when the boundary of the cross section consists of segments parallel to the coordinate axes. The extension of some of the dynamical results to the case that the intensity depends on time is discussed in the last section. (2000). 74H25, 74H40, 74G50. Mathematics Subject Classification

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