ERGODICITY CRITERIA FOR NON-EXPANDING TRANSFORMATIONS OF 2-ADIC SPHERESстатья
Статья опубликована в высокорейтинговом журнале
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Дата последнего поиска статьи во внешних источниках: 25 декабря 2013 г.
Аннотация:In the paper, we obtain necessary and sucient conditions for
ergodicity (with respect to the normalized Haar measure) of discrete dynamical
systems <f; S_{2^{-r}} (a)> on 2-adic spheres S_{2^{-r}} (a) of radius 2^{-r}, r \ge1, centered
at some point a from the ultrametric space of 2-adic integers Z_2. The map
f : Z_2\toZ_2 is assumed to be non-expanding and measure-preserving; that is,
f satises a Lipschitz condition with a constant 1 with respect to the 2-adic
metric, and f preserves a natural probability measure on Z_2, the Haar measure
\mu_2 on Z2 which is normalized so that \mu_2(Z_2) = 1.