Directional recurrence and directional rigidity for infinite measure preserving actions of nilpotent lattices
نویسندگان
چکیده
منابع مشابه
DIRECTIONAL RECURRENCE FOR INFINITE MEASURE PRESERVING Zd ACTIONS
We define directional recurrence for infinite measure preserving Z actions both intrinsically and via the unit suspension flow and prove that the two definitions are equivalent. We study the structure of the set of recurrent directions and show it is always a Gδ set. We construct an example of a recurrent action with no recurrent directions, answering a question posed in a 2007 paper of Daniel ...
متن کاملLinear Functions Preserving Multivariate and Directional Majorization
Let V and W be two real vector spaces and let &sim be a relation on both V and W. A linear function T : V → W is said to be a linear preserver (respectively strong linear preserver) of &sim if Tx &sim Ty whenever x &sim y (respectively Tx &sim Ty if and only if x &sim y). In this paper we characterize all linear functions T : M_{n,m} → M_{n,k} which preserve or strongly preserve multivariate an...
متن کاملMultiple and Polynomial Recurrence for Abelian Actions in Infinite Measure
We apply the (C, F )-construction from [Da] to produce a number of funny rank one infinite measure preserving actions of Abelian groups G with “unusual” multiple recurrence properties. In particular, we construct the following for each p ∈ N ∪ {∞}: (i) a p-recurrent action T = (Tg)g∈G such that (if p 6=∞) no one transformation Tg is (p + 1)-recurrent for every element g of infinite order, (ii) ...
متن کاملMeasurable Rigidity of Actions on Infinite Measure Homogeneous Spaces, Ii
Theorem 1.1 (Shalom and Steger, [21]). Measurable isomorphisms between linear actions on R of abstractly isomorphic lattices in SL2(R) are algebraic. More precisely, if τ : Γ1 ∼= −→Γ2 is an isomorphism between two lattices in SL2(R) and T : R → R is a measure class preserving map with T (γx) = γT (x) for a.e. x ∈ R and all γ ∈ Γ1, then there exists A ∈ GL2(R) so that γ = AγA−1 for all γ ∈ Γ1 an...
متن کاملExtensions and Multiple Recurrence of infinite measure preserving systems
We prove that an extension of an invertible, multiply-recurrent infinite measure preserving transformation is also multiply-recurrent.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Ergodic Theory and Dynamical Systems
سال: 2016
ISSN: 0143-3857,1469-4417
DOI: 10.1017/etds.2015.127