Topological friction in aperiodic minimal $\mathbb R^m$-actions
Volume 207 / 2010
Fundamenta Mathematicae 207 (2010), 175-178
MSC: Primary 37B05.
DOI: 10.4064/fm207-2-5
Abstract
For a continuous map $f$ preserving orbits of an aperiodic $\mathbb R^m$-action on a compact space, its displacement function assigns to $x$ the “time” $t \in \mathbb R^m$ it takes to move $x$ to $f(x)$. We show that this function is continuous if the action is minimal. In particular, $f$ is homotopic to the identity along the orbits of the action.
