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In the paper, we obtain necessary and sufficient conditions for ergodicity(with respect to the normalized Haar measure) of discrete dynamical systems$<f;\mathbf S_{2^{-r}}(a)>$ on 2-adic spheres $\mathbf S_{2^{-r}}(a)$ of radius$2^{-r}$, $r\ge 1$, centered at some point $a$ from the ultrametric space of2-adic integers $\mathbb Z_2$. The map $f\colon\mathbb Z_2\to\mathbb Z_2$ isassumed to be non-expanding and measure-preserving; that is, $f$ satisfies aLipschitz condition with a constant 1 with respect to the 2-adic metric, and$f$ preserves a natural probability measure on $\mathbb Z_2$, the Haar measure$\mu_2$ on $\mathbb Z_2$ which is normalized so that $\mu_2(\mathbb Z_2)=1$.

Ergodicity criteria for non-expanding transformations of 2-adic spheres