Shadowing vs. distality for actions of \(\mathbb R^n\). (English) Zbl 1251.37034
This article introduces the notion of weakly parametrized (wp) shadowing for actions of groups \(\mathbb Z^m\times \mathbb R^n\), where \(m,n \geq 0\) and \(m+n>0\). The possibility of coexistence of distality and shadowing for actions of \(\mathbb R^n\) is discussed. It is proven that an equicontinuous action of \(\mathbb R^n\) on a compact connected space possessing wp-shadowing is actually minimal. Moreover, distal real flows (\(\mathbb R\)-actions) on one-dimensional compact metric spaces are characterized as constant-one suspensions over adding machines.
Reviewer: Jerzy Ombach (Kraków)
MSC:
| 37C50 | Approximate trajectories (pseudotrajectories, shadowing, etc.) in smooth dynamics |
| 22F05 | General theory of group and pseudogroup actions |
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