The paper deals with hyperbolic homogeneous systems [Formula: see text] of partial differential equations with constant coefficients for an N-vector u(t,x1,...,xn). Here, P is a matrix form of order N and degree m. In the scalar case (N = 1), every hyperbolic P is limit of strictly hyperbolic ones. This does not hold for systems as is shown here for the special case N = n = 3, m = 2. Assuming P(1,0,...,0) to be the unit matrix, we represent P by a point in R81. The hyperbolic P form a closed set H in R81, the strictly hyperbolic ones an open subset Hs of H. An example is given for a P in H which is not in the closure of Hs. Moreover, it is shown that near that P the set H coincides with an algebraic manifold of codimension 4.
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机译：本文研究了N向量u（t，x1，...，xn）具有常数系数的偏微分方程的双曲齐次系统[公式]。这里，P是N阶和度m的矩阵形式。在标量情况下（N = 1），每个双曲P都是严格双曲P的极限。这不适用于系统，如特殊情况下N = n = 3，m = 2所示。假设P（1,0，...，0）为单位矩阵，我们用一个点表示P。 R81。双曲P在R81中形成闭集H，严格双曲P是 H 的开放子集 Hs 。给出了 H 中的 P 的示例，该示例不在 Hs 的闭包中。而且，表明在那个 P 附近，集合 H 与余维4的代数流形重合。
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