When the Favard separation condition fails, a linear almost periodic equation possessing bounded solutions may have no almost periodic solutions, or equivalently, no continuous solutions in hull. Almost automorphic solutions are however known to persist and, in the scalar case, the same happens to semi-continuous solutions in the hull. The aim of the present paper is twofold: extending the second type of solutions to higher dimensions, via the notion of barycenter, and fully understanding the relationships with the first type of solutions. Semi-continuity has to be replaced by some Baire class and the scalar connection with almost automorphy breaks down in an unrecoverable way: a not negligible effort is devoted to restore it at deeper level of generality.

中文翻译：

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线性概周期方程的重心解：Baire类和概自同构

当Favard分离条件失败时，具有有界解的线性几乎周期方程可能在壳体中没有几乎周期解，或者等效地，没有连续解。但是，已知几乎所有的自同构解都将持续存在，并且在标量情况下，船体中的半连续解也是如此。本文的目的是双重的：通过重心的概念将第二种解决方案扩展到更高的维度，并充分理解与第一类解决方案的关系。半连续性必须被某些Baire类所取代，几乎具有自态性的标量连接会以无法恢复的方式崩溃：要在更深层次的通用性上进行恢复，需要付出不可忽视的努力。