Family-independence for topological and measurable dynamics

Details Family-independence for topological and measurable dynamics Family-independence for topological and measurable dynamics

2009-08-05

arxiv.org/abs/0908.0574v2

Mathematics

Dynamical Systems

Minor change. To appear in Trans. Amer. Math. Soc

Scientific paper

For a family F (a collection of subsets of Z_+), the notion of F-independence is defined both for topological dynamics (t.d.s.) and measurable dynamics (m.d.s.). It is shown that there is no non-trivial {syndetic}-independent m.d.s.; a m.d.s. is {positive-density}-independent if and only if it has completely positive entropy; and a m.d.s. is weakly mixing if and only if it is {IP}-independent. For a t.d.s. it is proved that there is no non-trivial minimal {syndetic}-independent system; a t.d.s. is weakly mixing if and only if it is {IP}-independent. Moreover, a non-trivial proximal topological K system is constructed, and a topological proof of the fact that minimal topological K implies strong mixing is presented.

Affiliated with

Also associated with

No associations

Rating

Family-independence for topological and measurable dynamics does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Family-independence for topological and measurable dynamics, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Family-independence for topological and measurable dynamics will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-254184