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Orbit counting with an isometric direction

G. Everest·V. Stangoe·T. Ward
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Abstract

Analogues of the prime number theorem and Merten's theorem are well-known for dynamical systems with hyperbolic behaviour. In this paper a 3-adic extension of the circle doubling map is studied. The map has a 3-adic eigendirection in which it behaves like an isometry, and the loss of hyperbolicity leads to weaker asymptotic results on orbit counting than those obtained for hyperbolic maps.

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G. Everest, V. Stangoe, T. Ward. 2004-07-09. Orbit counting with an isometric direction. https://arxiv.org/abs/math/0407166

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