The existence problem for attractors of foliations with transverse linear connection is investigated. In general foliations with transverse linear connection do not admit attractors. Sufficient conditions are found for the existence of a global attractor that is a minimal set. An application to transversely similar pseudo-Riemannian foliations is obtained. The global structure of transversely similar Riemannian foliations is described. Different examples are constructed.

中文翻译：

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关于具有横向线性连接的整体叶子吸引子的存在

研究了具有横向线性连接的叶片吸引子的存在问题。通常，具有横向线性连接的叶不允许引入吸引子。发现存在最小集的全局吸引子的充分条件。获得了对横向相似的拟黎曼叶面的应用。描述了横向相似的黎曼叶面的整体结构。构建了不同的示例。