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arXiv · 1810.06708

Attractors associated to a family of hyperbolic $p$-adic plane automorphisms

Clayton Petsche
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Abstract

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.

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Clayton Petsche. 2018-10-15. Attractors associated to a family of hyperbolic $p$-adic plane automorphisms. https://arxiv.org/abs/1810.06708

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