# On uniform distribution of polynomials and good universality

(2020) On uniform distribution of polynomials and good universality. Ergodic Theory and Dynamical Systems, 40 (4). 992 - 1007.

## Abstract

Suppose (k(n))(n >= 1) is Hartman uniformly distributed and good universal. Also suppose psi is a polynomial with at least one coefficient other than psi(0) an irrational number. We adapt an argument due to Furstenberg to prove that the sequence (psi(k(n)))(n >= 1) is uniformly distributed modulo one. This is used to give some new families of Poincar ' e recurrent sequences. In addition we show these sequences are also intersective and Glasner.

Item Type: Article Symplectic Admin 07 Aug 2018 06:11 16 Apr 2021 11:43 10.1017/etds.2018.53 Publisher https://livrepository.liverpool.ac.uk/id/eprint/3024657