We study topological properties of automorphisms of 4-dimensional torus generatedby integer matrices being symplectic either with respect to the standard symplecticstructure in R4 or w.r.t. a nonstandard symplectic structure generated by an integer skew-symmetric nondegenerate matrix. Such symplectic matrix generates a partiallyhyperbolic automorphism of the torus, if its eigenvalues are a pair of reals outsidethe unit circle and a complex conjugate pair on the unit circle. The main classifying element is the topology of a foliation generated by unstable (stable) leaves ofthe automorphism. There are two different cases, transitive and decomposable ones.For the first case the foliation into unstable (stable) leaves is transitive, for the second case the foliation itself has a sub-foliation into 2-dimensional tori. For both cases the classification is given.

中文翻译：

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4-圆环上辛部分双曲自同构的几何

我们研究了由整数矩阵辛生成的 4 维环的自同构的拓扑性质，要么相对于 R4 中的标准辛结构，要么是由整数斜对称非退化矩阵生成的非标准辛结构。如果其特征值是单位圆外的一对实数和单位圆上的复共轭对，则这种辛矩阵生成环面的部分双曲自同构。主要的分类元素是由自同构的不稳定（稳定）叶生成的叶理的拓扑结构。有两种不同的情况，可传递的和可分解的。对于第一种情况，叶理变成不稳定（稳定）叶子是可传递的，对于第二种情况，叶理本身有一个子叶理成二维环面。