Let G = PSL2(F) where F = R,C, and consider the space Z = (Γ1 × Γ2)\(G × G) where Γ1 < G is a co-compact lattice and Γ2 < G is a finitely generated discrete Zariski dense subgroup. The work of Benoist-Quint [2] gives a classification of all ergodic invariant Radon measures on Z for the diagonal G-action. In this paper, for a horospherical subgroup N of G, we classify all ergodic, conservative, ...

The classical ergodic theory hasbeen built on σ-algebras. Later the Individual ergodictheorem was studied on more general structures like MV-algebrasand quantum structures. The aim of this paper is to formulate theIndividual ergodic theorem for intuitionistic fuzzy observablesusing  m-almost everywhere convergence, where  m...

Let J be the repeller of an expanding, C 1þd-conformal topological mixing map g: Let F : J ! R d be a continuous function and let aðxÞ ¼ lim n!1 1 n P nÀ1 j¼0 Fðg j xÞ (when the limit exists) be the ergodic limit. It is known that the possible aðxÞ are just the values R F dm for all g-invariant measures m: For any a in the range of the ergodic limits, we prove the following variational formula:...

We prove that for all ergodic extensions S1 of a transformation by a locally compact second countable group G, and for all G-extensions S2 of an aperiodic transformation, there is a relative speedup of S1 that is relatively isomorphic to S2. We apply this result to give necessary and sufficient conditions for two ergodic n-point or countable extensions to be related in this way.

For an ergodic p.m.p. action G y (X,μ) of a countable group G, we define the Rokhlin entropy hRok G (X,μ) to be the infimum of the Shannon entropies of countable generating partitions. It is known that for free ergodic actions of amenable groups this notion coincides with classical Kolmogorov– Sinai entropy. It is thus natural to view Rokhlin entropy as a close analogue to classical entropy. Un...

This paper deals with some self-interacting diffusions (Xt, t ≥ 0) living on R. These diffusions are solutions to stochastic differential equations: dXt = dBt − g(t)∇V (Xt − μt)dt, where μt is the mean of the empirical measure of the process X , V is an asymptotically strictly convex potential and g is a given function. We study the ergodic behavior of X and prove that it is strongly related to...

We define the notion of uniformly recurrent subgroup, URS in short, which is a topological analog of the notion of invariant random subgroup (IRS), introduced in [2]. Our main results are as follows. (i) It was shown in [26] that for an arbitrary countable infinite group G, any free ergodic probability measure preserving G-system admits a minimal model. In contrast we show here, using URS’s, th...

Abstract We prove that the solid ergodicity property is stable with respect to taking coinduction for a fairly large class of coinduced action. More precisely, assume $\Sigma &amp;lt;\Gamma $ are countable groups such $g\Sigma g^{-1}\cap \Sigma finite any $g\in \Gamma \setminus $. Then measure preserving action \curvearrowright X_0$ gives rise solidly ergodic equivalence relation if and only as...

If G Alt(N) is an inductive limit of finite alternating groups, then the indecomposable characters of G are precisely the associated characters of the ergodic invariant random subgroups of G.

In the paper we completely describe characters (central positive-definite functions) of simple locally finite groups that can be represented as inductive limits of (products of) symmetric groups under block diagonal embeddings. Each such group G defines an infinite graded graph that encodes the embedding scheme. The group G acts on the space X of infinite paths of the associated graph by changi...