Topological friction in aperiodic minimal $\mathbb R^m$-actions

Tom 207 / 2010

Jarosław Kwapisz Fundamenta Mathematicae 207 (2010), 175-178 MSC: Primary 37B05. DOI: 10.4064/fm207-2-5

Streszczenie

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.

Autorzy

  • Jarosław KwapiszDepartment of Mathematical Sciences
    Montana State University
    Bozeman, MT 59717-2400, U.S.A.
    e-mail

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