Measure-Preservation and the Existence of a Root of p-Adic 1-Lipschitz Functions in Mahler’s Expansion

Аннотация

In this paper, we provide necessary and sufficient conditions for 1-Lipschitz functions that are uniformly differentiable mod p on ℤ_p to be measure-preserving, in Mahler’s expansion, and show that these conditions can be modified to guarantee the existence of a root of p-adic Lipschitz functions.