Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6424718 | Topology and its Applications | 2013 | 12 Pages |
Abstract
We show that for any abelian group G of affine maps on Cn, there exists a G-invariant affine subspace E of Cn such that E contains all elements of Cn on which G acts identically, the closure of every orbit in E is a minimal set of G/E and if Eâ Cn, there are G-invariant affine subspaces H1,â¦,Hs (1⩽s⩽nâdim(E)) of Cn of dimension nâ1 such that the closure of every orbit in U=Cn\âk=1sHk is a minimal set of G/U. Moreover, if G has a dense orbit, all orbits in U are dense in Cn.
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
Authors
Adlene Ayadi, Yahya Nʼdao,