Orbits on a nilmanifold under the action of a polynomial sequence of translations. (English) Zbl 1121.37005
Let \(g\) be a polynomial sequence of translations of a compact nilmanfold \(X\) and let \(A\) be the group generated by the elements of \(g\). It is shown that for almost all points \(x\in X\), the closures of orbits of points \(x\) under the action of \(g\) are congruent to the connected components of the closure of orbits of the points \(x\) under the action of \(A\).
Reviewer: Michael L. Blank (Moskva)
MSC:
37A15 | General groups of measure-preserving transformations and dynamical systems |
22F30 | Homogeneous spaces |
28D15 | General groups of measure-preserving transformations |