A zero-one law for dynamical properties

Details A zero-one law for dynamical properties A zero-one law for dynamical properties

1996-12-09

arxiv.org/abs/math/9612222v1

Mathematics

Dynamical Systems

Scientific paper

For any countable group $\Gamma$ satisfying the ``weak Rohlin property'', and for any dynamical property, the set of $\Gamma$-actions with that property is either residual or meager. The class of groups with the weak Rohlin property includes each lattice $\integers^{\times{d}}$; indeed, all countable discrete amenable groups. For $\Gamma$ an arbitrary countable group, let $\actsp$ be the set of $\Gamma$-actions on the unit circle $Y$. We establish an Equivalence theorem by showing that a dynamical property is Baire/meager/residual in $\actsp$ if and only if it is Baire/meager/residual in the set of shift-invariant measures on the product space $Y^{\times\Gamma}$.

Affiliated with

Also associated with

No associations

Rating

A zero-one law for dynamical properties 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 A zero-one law for dynamical properties, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A zero-one law for dynamical properties will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-633466