Abstract. This paper proves various results concerning non-ergodic actions of locally compact groups and particularly Borel cocycles defined over such actions. The general philosophy is to reduce the study of the cocycle to the study of its restriction to each ergodic component of the action, while being careful to show that all objects arising in the analysis depend measurably on the ergodic c...

Let G be a connected Lie group and let F be a lattice in G (not necessarily co-compact). We show that if («,) is a unipotent one-parameter subgroup of G then every ergodic invariant (locally finite) measure of the action of («,) on G/Y is finite. For 'arithmetic lattices' this was proved in [2]. The present generalization is obtained by studying the 'frequency of visiting compact subsets' for u...

Let {Xn} be a stationary and ergodic time series taking values from a finite or countably infinite set X and that f(X) is a function of the process with finite second moment. Assume that the distribution of the process is otherwise unknown. We construct a sequence of stopping times λn along which we will be able to estimate the conditional expectation E(f(Xλn+1)|X0, . . . , Xλn) from the observ...

We prove the effective version of Birkhoff’s ergodic theorem for Martin-Löf random points and effectively open sets, improving the results previously obtained in this direction (in particular those of V. Vyugin, Nandakumar and Hoyrup, Rojas). The proof consists of two steps. First, we prove a generalization of Kučera’s theorem, which is a particular case of effective ergodic theorem: a trajecto...

We investigate ergodic theory of Poisson suspensions. In the process, we establish close connections between finite and infinite measure preserving ergodic theory. Poisson suspensions thus provide a new approach to infinite measure ergodic theory. Fields investigated here are mixing properties, spectral theory, joinings. We also compare Poisson suspensions to the apparently similar looking Gaus...

in this paper by use of mathematical modeling of an observer [14,15] the notion of relative information functional for relative dynamical systemson compact metric spaces is presented. we extract the information function ofan ergodic dynamical system (x,t) from the relative information of t fromthe view point of observer χx, where x denotes the base space of the system.we also generalize the inv...

Abstract Packing topological entropy is a dynamical analogy of the packing dimension, which can be viewed as counterpart Bowen entropy. In present paper we give systematic study for continuous G -action system $(X,G)$ , where X compact metric space and countable infinite discrete amenable group. We first prove variational principle entropy: any Borel subset Z equals supremum upper local over al...