We consider a certain two-parameter family of automorphisms of the affine plane over a complete, locally compact non-Archimedean field. Each of these automorphisms admits a chaotic attractor on which it is topologically conjugate to a full two-sided shift map, and the attractor supports a unit Borel measure which describes the distribution of the forward orbit of Haar-almost all points in the basin of attraction. We also compute the Hausdorff dimension of the attractor, which is non-integral.

中文翻译：

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与一族双曲进阶平面自同构相关的吸引子

我们考虑在一个完整的、局部紧致的非阿基米德场上的仿射平面的某个二参数自同构族。这些自同构中的每一个都承认一个混沌吸引子，在该吸引子上它在拓扑上与一个完整的双边位移图共轭，并且该吸引子支持一个单位 Borel 度量，该度量描述了 Haar 的前向轨道的分布——几乎所有点在吸引力盆地中. 我们还计算了吸引子的 Hausdorff 维数，它是非整数的。