In this paper,it is shown that for a minimal system(X,G),if H is a normal subgroup of G with finite index n,then X can be decomposed into n components of closed sets such that each component is minimal under H-action....In this paper,it is shown that for a minimal system(X,G),if H is a normal subgroup of G with finite index n,then X can be decomposed into n components of closed sets such that each component is minimal under H-action.Meanwhile,we prove that for a residual set of points in a minimal system with finitely many commuting homeomorphisms,the set of return times to any non-empty open set contains arbitrarily long geometric progressions in multidimension,extending a previous result by Glasscock,Koutsogiannis and Richter.展开更多
文摘In this paper,it is shown that for a minimal system(X,G),if H is a normal subgroup of G with finite index n,then X can be decomposed into n components of closed sets such that each component is minimal under H-action.Meanwhile,we prove that for a residual set of points in a minimal system with finitely many commuting homeomorphisms,the set of return times to any non-empty open set contains arbitrarily long geometric progressions in multidimension,extending a previous result by Glasscock,Koutsogiannis and Richter.
