Geometrically simple Bernoulli generators are constructed for certain ergodic endomorphisms of solenoids. An arbitrary ergodic solenoidal group automorphism is obtained as the limit of a sequence of such Bernoulli factors and hence, by a theorem of D. S. Ornstein, must be measuretheoretically isomorphic to a Bernoulli shift. In his survey paper [6], B. Weiss stated that, using Y. Katznelson's m...

We establish convergence in norm and pointwise almost everywhere for the non-conventional (in sense of Furstenberg) bilinear polynomial ergodic averages $$ A_N(f,g)(x) := \frac{1}{N} \sum_{n=1}^{N} f(T^nx) g(T^{P(n)}x) as $N \to \infty$, where $T\colon X\to X$ is a measure-preserving transformation $\sigma$-finite measure space $(X,\mu), P(\mathrm{n})\in \mathbb{Z}[\mathrm{n}]$ degree $d \geq 2...

In this note we give a short proof of a pointwise ergodic theorem for measure preserving actions of word hyperbolic groups, also obtained recently by Bufetov, Khristoforov and Klimenko. Our approach also applies to infinite measure spaces and one application is to linear actions of discrete groups on the plane. 0. Introduction The well-known Birkhoff ergodic theorem for ergodic transformations ...

We present a comprehensive analysis of the ergodic capacity and information outage probability of multipleinput multiple-output (MIMO) keyhole channels with antenna selection. In this regard, we consider several different scenarios with perfect channel state information (CSI) at the receiver and no, partial or full CSI at the transmitter. For all cases, we derive exact analytical closed-form ex...

The forward estimation problem for stationary and ergodic time series {X n } ∞ n=0 taking values from a finite alphabet X is to estimate the probability that X n+1 = x based on the observations X i , 0 ≤ i ≤ n without prior knowledge of the distribution of the process {X n }. We present a simple procedure g n which is evaluated on the data)| → 0 almost surely for a subclass of all stationary an...

For nonconformal repellers satisfying a certain cone condition, we establish a version of multifractal analysis for the topological entropy of the level sets of the Lyapunov exponents. Due to the nonconformality, the Lyapunov exponents are averages of nonadditive sequences of potentials, and thus one cannot use Birkhoff’s ergodic theorem neither the classical thermodynamic formalism. We use ins...

Given ergodic p-invariant measures f i g on the 1-torus T = R=Z, we give a sharp condition on their entropies, guaranteeing that the entropy of the convolution 1 n converges to log p. We also prove a variant of this result for joinings of full entropy on T N. In conjunction with a method of Host, this yields the following. Denote q (x) = qx (mod 1). Then for every p-invariant ergodic with posit...

An IFS (iterated function system) such that there exists a positive bounded function h : [0, 1] → R and a probability ν on [0, 1] satisfying P u (h) = ρh, P * u (ν) = ρν. There is no meaning to ask if the probabilities ν on [0, 1] arising in IFS are invariant for a dynamical system, but, we can ask if probabil-itiesˆν on [0, 1] × Σ are holonomic forˆσ. A probabilityˆν on [0, 1] × Σ is called ho...

0. Introduction. Let Kn denote the «-dimensional torus. Let 7 be an affine transformation of Kn onto Kn and S an affine transformation of Km onto Km for which there exists a continuous map h of Kn onto Km satisfying hT= Sh. R. L. Adler and R. Palais have proved that, in the special cases when m = n and 7 and S are ergodic automorphisms of Kn, all homeomorphism g of Kn, satisfying gT= Sg, are af...

I G. Kallianpur and H. Robbins, "Ergodic Property of the Brownian Motion Process," these PROCEEDINGS, 39, 525-533, 1953, and "The Sequence of Sums of Independent Random Variables," I)uke Alath. J. 21, 285-308, 1954. 2 H. Robbins, "On the Equidistribution of Sums of Independent Random Variables," Proc. Aml. Math. Soc., 4, 786-799, 1953. 3 T. E. Harris and H. Robbins, "Ergodic Theory of Markov Ch...