共查询到20条相似文献,搜索用时 62 毫秒
1.
Wolfgang Krieger 《Israel Journal of Mathematics》1987,60(2):167-176
The results ofOn sofic systems I on topological Markov chains extending sofic systems are completed. To homomorphisms of sofic systems are canonically associated
homomorphisms of Markov extensions. Also considered is a class of finitary codes for sofic systems. 相似文献
2.
Liviu P?unescu 《Journal of Functional Analysis》2011,261(9):2461-2485
The notion of sofic equivalence relation was introduced by Gabor Elek and Gabor Lippner. Their technics employ some graph theory. Here we define this notion in a more operator algebraic context, starting from Connes? Embedding Problem, and prove the equivalence of these two definitions. We introduce a notion of sofic action for an arbitrary group and prove that an amalgamated product of sofic actions over amenable groups is again sofic. We also prove that an amalgamated product of sofic groups over an amenable subgroup is again sofic. 相似文献
3.
A symbolic flow is called a sofic system if it is a homomorphic image (factor) of a subshift of finite type. We show that every sofic system can be realized as a finite-to-one factor of a subshift of finite type with the same entropy. From this it follows that sofic systems share many properties with subshifts of finite type. We concentrate especially on the properties of TPPD (transitive with periodic points dense) sofic systems. 相似文献
4.
Wolfgang Krieger 《Israel Journal of Mathematics》1984,48(4):305-330
Topological Markov chains are invariantly associated with sofic systems. A dimension function is introduced for sofic systems,
and a criterion is given for a sofic system to be properly sofic. 相似文献
5.
Luiz Cordeiro 《Comptes Rendus Mathematique》2018,356(9):957-962
We prove that the class of sofic groupoids is stable under several measure-theoretic constructions. In particular, we show that virtually sofic groupoids are sofic. We answer a question of Conley, Kechris, and Tucker-Drob by proving that an aperiodic pmp groupoid is sofic if and only if its full group is metrically sofic. 相似文献
6.
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
7.
We investigate a notion of soficity for monoids. A group is sofic as a group if and only if it is sofic as a monoid. All finite monoids, all commutative monoids, all free monoids, all cancellative one-sided amenable monoids, all multiplicative monoids of matrices over a field, and all monoids obtained by adjoining an identity element to a semigroup are sofic. On the other hand, although the question of the existence of a non-sofic group remains open, we prove that the bicyclic monoid is not sofic. This shows that there exist finitely presented amenable inverse monoids that are non-sofic. 相似文献
8.
Guohua Zhang 《Journal of Functional Analysis》2012,262(4):1954-1985
Recently Lewis Bowen introduced a notion of entropy for measure-preserving actions of countable sofic groups admitting a generating measurable partition with finite entropy; and then David Kerr and Hanfeng Li developed an operator-algebraic approach to actions of countable sofic groups not only on a standard probability space but also on a compact metric space, and established the global variational principle concerning measure-theoretic and topological entropy in this sofic context. By localizing these two kinds of entropy, in this paper we prove a local version of the global variational principle for any finite open cover of the space, and show that these local measure-theoretic and topological entropies coincide with their classical counterparts when the acting group is an infinite amenable group. 相似文献
9.
We classify certain sofic shifts (the irreducible Point Extension Type, or PET, sofic shifts) up to flow equivalence, using invariants of the canonical Fischer cover. There are two main ingredients.
相似文献
- (1)An extension theorem, for extending flow equivalences of subshifts to flow equivalent irreducible shifts of finite type which contain them.
- (2)The classification of certain constant to one maps from SFTs via algebraic invariants of associated G-SFTs.
10.
We introduce mean dimensions for continuous actions of countable sofic groups on compact metrizable spaces. These generalize the Gromov–Lindenstrauss–Weiss mean dimensions for actions of countable amenable groups, and are useful for distinguishing continuous actions of countable sofic groups with infinite entropy. 相似文献
11.
A sofic system is a symbolic flow defined by a finite semigroup. We exhibit finite procedures, involving only the defining semigroup, for answering cetain questions about a sofic system and for constructing certain subshifts of finite type associated with a sofic system. 相似文献
12.
Angela Desai 《Indagationes Mathematicae》2006,17(3):353-359
We prove that any ?d shift of finite type with positive topological entropy has a family of subsystems of finite type whose entropies are dense in the interval from zero to the entropy of the original shift. We show a similar result for ?d sofic shifts, and also show every ?d sofic shift can be covered by a ?d shift of finite type arbitrarily close in entropy. 相似文献
13.
We construct an analogue of von Neumann's affiliated algebras for sofic group algebras over arbitrary fields. Consequently, we settle Kaplansky's direct finiteness conjecture for sofic groups. 相似文献
14.
我们对复Banach空间上的可数sofic群的等距线性作用提出了一种新的维数,推广了复Banach空间上的可数顺从群的等距线性作用的Voiculescu维数,并且在可数sofic群的情形回答了Gromov的一个问题. 相似文献
15.
《Chaos, solitons, and fractals》2000,11(1-3):315-319
16.
Paul Trow 《Monatshefte für Mathematik》1998,125(4):327-342
We define a class of factor maps between sofic shifts, called lifting maps, which generalize the closing maps. We show that an irreducible sofic shiftS has only finitely manyS-conjugacy classes of minimal left (or right) lifting covers. The number of these classes is a computable conjugacy invariant ofS. Furthermore, every left lifting cover factors through a minimal left lifting cover. 相似文献
17.
We prove that Connes Embedding Conjecture holds for the von Neumann algebras of sofic groups, that is sofic groups are hyperlinear. Hence we provide some new examples of hyperlinearity. We also show that the Determinant Conjecture holds for sofic groups as well. We introduce the notion of essentially free actions and amenable actions and study their properties.Mathematics Subject Classification (2000): 43A07, 55N25 相似文献
18.
We prove a number of identities relating the sofic entropy of a certain class of non-expansive algebraic dynamical systems, the sofic entropy of the Wired Spanning Forest and the tree entropy of Cayley graphs of residually finite groups. We also show that homoclinic points and periodic points in harmonic models are dense under general conditions. 相似文献
19.
Prof. Dr. Roland Fischer 《Monatshefte für Mathematik》1975,80(3):179-186
A subclass of the class of the subshifts of finite-state symbolic shifts, which was introduced byB. Weiss under the name “sofic systems”, is characterized and studied by using graphs. It is proved that topologically transitive sofic systems are intrinsically ergodic. 相似文献
20.
In this article, subsets of \({\mathbb {N}}\) that can arise as sets of periods of the following subshifts are characterized: (i) subshifts of finite type, (ii) transitive subshifts of finite type, (iii) sofic shifts, (iv) transitive sofic shifts, and (v) arbitrary subshifts. 相似文献