2018/10/15 by Clayton Petsche, Petsche, Clayton
Mathematics · #11S82 #37B10 #37D20 #37D45 #37F35 #37P20 #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT) #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.1810.06708
openalex publication_date 2018/10/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.