Shadowing vs. distality for actions of ℝ.

This article introduces the notion of weakly parametrized (wp) shadowing for actions of groups ℤ m  × ℝ n , where m, n ≥ 0 and m + n > 0. The possibility of coexistence of distality and shadowing for actions of ℝ n is discussed. It is proven that an equicontinuous action of ℝ n on a compact connected space possessing wp-shadowing is actually minimal. Moreover, distal real flows (ℝ-actions) on one-dimensional compact metric spaces are characterized as constant-one suspensions over adding machines. [ABSTRACT FROM PUBLISHER]