On Dynamics of Infinitely Generated Contractive Mapping Systems on pℤp.

Let p ≥ 2 be a prime number and ℤp be the ring of p-adic intergers. Let G be a semigroup generated by infinitely many contractive maps on pℤp. It is shown that if G satisfies the open tiling conditions, then there exists a shift transformation on the limit set of G and the shift transformation is ergodic with respect to the Haar measure on pℤp. As an application, we can generalize p-adic Khinchin's Theorem and p-adic Lochs' Theorem to any infinitely generated semigroup by use of the ergodicity of the shift transformation. [ABSTRACT FROM AUTHOR]