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Orbit counting with an isometric direction

2005; American Mathematical Society; Linguagem: Inglês

10.1090/conm/385/07202

1098-3627

Graham Everest, V. Stangoe, Thomas Ward,

Cellular Automata and Applications

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.