共查询到20条相似文献,搜索用时 15 毫秒
1.
Christopher Deninger 《Journal of the American Mathematical Society》2006,19(3):737-758
In 1990, Lind, Schmidt, and Ward gave a formula for the entropy of certain -dynamical systems attached to Laurent polynomials , in terms of the (logarithmic) Mahler measure of . We extend the expansive case of their result to the noncommutative setting where gets replaced by suitable discrete amenable groups. Generalizing the Mahler measure, Fuglede-Kadison determinants from the theory of group von Neumann algebras appear in the entropy formula.
2.
Pavel Zorin-Kranich 《Israel Journal of Mathematics》2014,204(1):85-96
We extend Bourgain’s return times theorem to arbitrary locally compact second countable amenable groups. The proof is based on a version of the Bourgain-Furstenberg-Katznelson-Ornstein orthogonality criterion. 相似文献
3.
Bowen introduced a definition of topological entropy of subset inspired by Hausdorff dimension in 1973 [1]. In this paper we consider the Bowen entropy for amenable group action dynamical systems and show that, under the tempered condition, the Bowen entropy of the whole compact space for a given Følner sequence equals the topological entropy. For the proof of this result, we establish a variational principle related to the Bowen entropy and the Brin–Katok local entropy formula for dynamical systems with amenable group actions. 相似文献
4.
A. Rosenthal 《Probability Theory and Related Fields》1988,77(2):147-166
Summary Let (X) be a Lebesgue space. We prove in the first part of this paper that any ergodic 2-action on (X) with finite entropy hLogk has generating partition P that is uniform and has k atoms. In the second part, we prove a similar result for any ergodic, free G-action with finite entropy hLog(k-2), for any discrete amenable group G. 相似文献
5.
Let G be a countable discrete infinite amenable group which acts continuously on a compact metric space X and let μ be an ergodic G-invariant Borel probability measure on X. For a fixed tempered F?lner sequence {Fn} in G with limn→+∞|Fn|/log n= ∞, we prove the following result:h_top~B(G_μ, {F_n}) = h_μ(X, G),where G_μ is the set of generic points for μ with respect to {F_n} and h_top~B(G_μ, {F_n}) is the Bowen topological entropy(along {F_n}) on G_μ. This generalizes the classical result of Bowen(1973). 相似文献
6.
Mathematische Zeitschrift - Let R be a ring, let G be an amenable group and let $$R{*}G$$ be a crossed product. The goal of this paper is to construct, starting with a suitable additive function L... 相似文献
7.
Iddo Samet 《Israel Journal of Mathematics》2009,173(1):61-90
Given a countable discrete amenable group G, does there exist a free action of G on a Lebesgue probability space which is both rigid and weakly mixing? The answer to this question is positive if G is abelian. An affirmative answer is given in this paper, in the case that G is solvable or residually finite. For a locally finite group, the question is reduced to an algebraic one. It is exemplified how the algebraic question can be positively resolved for some groups, whereas for others the algebraic viewpoint suggests the answer may be negative. 相似文献
8.
Marie Choda 《Journal of Functional Analysis》2004,217(1):181-191
Let G⊂Aut(A) be a discrete group which is exact, that is, admits an amenable action on some compact space. Then the entropy of an automorphism of the algebra A does not change by the canonical extension to the crossed product A×G. This is shown for the topological entropy of an exact C∗-algebra A and for the dynamical entropy of an AFD von Neumann algebra A. These have applications to the case of transformations on Lebesgue spaces. 相似文献
9.
Donald Robertson 《Journal d'Analyse Mathématique》2016,129(1):165-196
We describe characteristic factors for certain averages arising from commuting actions of locally compact second-countable amenable groups. Under some ergodicity assumptions, we use these factors to prove a form of multiple recurrence for three such actions. 相似文献
10.
In this note we show that the entropy of a skew product action of a countable amenable group satisfies the classical formula of Abramov and Rokhlin. 相似文献
11.
12.
The local properties of entropy for a countable discrete amenable group action are studied. For such an action, a local variational principle for a given finite open cover is established, from which the variational relation between the topological and measure-theoretic entropy tuples is deduced. While doing this it is shown that two kinds of measure-theoretic entropy for finite Borel covers coincide. Moreover, two special classes of such an action: systems with uniformly positive entropy and completely positive entropy are investigated. 相似文献
13.
Let be a lattice in a noncompact simple Lie Group G, where . Suppose acts analytically and ergodically on a compact manifold M preserving a unimodular rigid geometric structure (e.g. a connection and a volume). We show that either the action is isometric or there exists a "large image" linear representation of . Under an additional assumption on the dynamics of the action, we associate to a virtual arithmetic quotient of full entropy.
Received: December 14, 2000 相似文献
14.
Toshihiko Masuda 《Proceedings of the American Mathematical Society》1999,127(7):2053-2057
Using the continuous decomposition, we classify strongly free actions of discrete amenable groups on strongly amenable subfactors of type III, . Winsløw's fundamental homomorphism is a complete invariant. This removes the extra assumptions in the classification theorems of Loi and Winsløw and gives a complete classification up to cocycle conjugacy.
15.
Robert J. Zimmer 《Israel Journal of Mathematics》1991,75(1):65-80
We show that many natural classes of actions of discrete subgroups of semisimple Lie groups have discrete spectrum, i.e.,
are measurably conjugate to isometric actions.
Research partially supported by NSF Grant. 相似文献
16.
Roland Vergnioux 《Journal of Functional Analysis》2004,212(1):206-221
The basic notions and results of equivariant KK-theory concerning crossed products can be extended to the case of locally compact quantum groups. We recall these constructions and prove some useful properties of subgroups and amalgamated free products of discrete quantum groups. Using these properties and a quantum analogue of the Bass-Serre tree, we establish the K-amenability of amalgamated free products of amenable discrete quantum groups. 相似文献
17.
Christopher Dwyer 《K-Theory》2008,38(2):95-111
We will make a construction of twisted equivariant K-theory for proper actions of discrete groups by using ideas of Lück and Oliver (Topology 40:585–616, 2001) to expand a construction
of Adem and Ruan (Comm. Math. Phys. 237:533–556, 2003). 相似文献
18.
David Kerr 《Israel Journal of Mathematics》2014,202(1):461-474
We prove that every Bernoulli action of a sofic group has completely positive entropy with respect to every sofic approximation net. We also prove that every Bernoulli action of a finitely generated free group has the property that each of its nontrivial factors with a finite generating partition has positive f-invariant. 相似文献
19.
Translated from Teoriya Funktsii, Funktsional'nyi Analiz i Ikh Prilozheniya, No. 51, pp. 117–122, 1989. 相似文献
20.
Yoshinobu Kamishima 《Topology and its Applications》1985,19(2):189-199
This note will concern properly discontinuous actions of subgroups in real algebraic groups on contractible manifolds. Let (π,X,ρ) be such an action, where ρ:π→ Diff(X) is a homomorphism. We assume that ? extends to a smooth action of a real algebraic group G containing π. If such π has a nontrivial radical (i.e., unique maximal normal solvable subgroup), then we can apply the method of Seifert construction [14],[17] to yield that the quotient π\X supports the structure of an injective Seifert fibering with typical (resp. exceptional) fiber diffeomorphic to a solv (resp. infrasolv)-manifold (when π acts freely). When G is an amenable algebraic group, we can say about a uniqueness property for such actions. Namely, let (πi, Xi, ρi) be actions as above (i= 1,2). Then, given an isomorphism f of π1 onto ?2, there is a diffeomorphism h: X1→X2 such that h(ρ1(r)x)=ρ2(f(r)h(x).As an application, we try to decide the structure of affine motions of some euclidean space n. First we verify the conjecture of [17, 4 5], i.e., a compact complete affinely flat manifold admits a maximal toral action if its fundamental group has a nontrivial center. Second, a compact complete affinity flat manifold whose fundamental group is virtually polycyclic supports the structure of an infrasolvmanifold. This structure varies depending on its solvable kernel (if it is abelian or nilpotent, it must be a euclidean space form or an infranilmanifold respectively). If a group of the affine group A(n) acts properly discontinuously and with compact quotient of n, then it is called an affine crystallographic group. Finally, we can say so far as to a uniqueness property that two virtually polycyclic affine crystallographic groups are conjugate inside Diff(n) if they are isomorphic (cf.[8]). 相似文献