Orbit counting with an isometric direction

Details Orbit counting with an isometric direction Orbit counting with an isometric direction

2004-07-09

arxiv.org/abs/math/0407166v1

Contemporary Mathematics, 385, 293-302, 2005

Mathematics

Dynamical Systems

Scientific paper

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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