Attractors associated to a family of hyperbolic $p$-adic plane automorphisms. (arXiv:1810.06708v1 [math.DS])

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 topolgocally conjugate to the 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. 查看全文>>