Erogdic decompostion for a class of B-functions on the ring of p-adic integers

초록

In this talk, we present an ergodicity criterion of a certain class of 1-Lipschitz functions on Zp for arbitrary primes p, known as B-functions . Thus, a complete description of ergodic polynomials modulo p μ , is provided where μ = μ(p) = 3 for p ∈ {2, 3} and μ = 2 for p ≥ 5. If time permits, we also present some ergodicity criteria for 1-Lipschitz functions on Zp, in terms of the van der Put coefficients as well as the inherent data associated with the function. These criteria are applied to provide sufficient conditions for ergodicity of the 1-Lipschitz p-adic functions with special features, such as everywhere/uniform differentiability with respect to the Mahler expansion.