In the paper, we obtain necessary and sufficient conditions for ergodicity
(with respect to the normalized Haar measure) of discrete dynamical systems
on 2-adic spheres S2βrβ(a) of radius
2βr, rβ₯1, centered at some point a from the ultrametric space of
2-adic integers Z2β. The map f:Z2ββZ2β is
assumed to be non-expanding and measure-preserving; that is, f satisfies a
Lipschitz condition with a constant 1 with respect to the 2-adic metric, and
f preserves a natural probability measure on Z2β, the Haar measure
ΞΌ2β on Z2β which is normalized so that ΞΌ2β(Z2β)=1