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Attractors associated to a family of hyperbolic $p$-adic plane automorphisms
Part of
CLAYTON PETSCHE
Journal:

Ergodic Theory and Dynamical Systems / Volume 41 / Issue 6 / June 2021

Published online by Cambridge University Press:

20 February 2020, pp. 1867-1882

Print publication:

June 2021
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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.