We develop an efficient Eulerian numerical approach to extract invariant sets in a continuous dynamical system in the extended phase space (the x− t space). We extend the idea of ergodic partition and propose a concept called coherent ergodic partition for visualizing ergodic components in a continuous flow. Numerically, we first apply the level set method [33] and extend the backward phase flo...

Answering a question raised by Glasner and Rudolph (1984) we construct uncountably many strictly ergodic topological systems which are metrically isomorphic to a given ergodic system (X,63, #, T) but not almost topologically conjugate to it.

In this Note, we study the multiple ergodic averages of a locally constant real-valued function in linear Cookie-Cutter dynamical systems. The multifractal spectrum of these multiple ergodic averages is completely determined. §

A simple proof of Kingman’s subadditive ergodic theorem is developed from a point of view which is conceptually algorithmic and which does not rely on either a maximal inequality or a combinatorial Riesz lemma.

This thesis aims to investigate the capacity and bit error rate (BER) performance of multi-user diversity systems with random number of users and considers its application to cognitive radio systems. Ergodic capacity, normalized capacity, outage capacity, and average bit error rate metrics are studied. It has been found that the randomization of the number of users will reduce the ergodic capac...

The foundation of statistical mechanics and the explanation of the success of its methods rest on the fact that the theoretical values of physical quantities (phase averages) may be compared with the results of experimental measurements (infinite time averages). In the Thirties, this problem, called the ergodic problem, was dealt with by an ergodic theory that tried to resolve the problem by ma...

A Markov channel is a discrete information channel that includes as special cases the finite state channels and finite state codes of information theory. Kieffer and Rahe proved that one-sided and two-sided Markov channels have the following property: If the input source to a Markov channel is asymptotically mean stationary (AMS), then so is the resulting input-output process and hence the ergo...

We prove a conditioned version of the ergodic theorem for Markov processes, which we call a quasi-ergodic theorem. We also prove a convergence result for conditioned processes as the conditioning event becomes rarer.

We consider the extent to which one can compute bounds on the rate of convergence of a sequence of ergodic averages. It is not difficult to construct an example of a computable Lebesgue-measure preserving transformation of [0, 1] and a characteristic function f = χA such that the ergodic averages Anf do not converge to a computable element of L ([0, 1]). In particular, there is no computable bo...

We consider the extent to which one can compute bounds on the rate of convergence of a sequence of ergodic averages. It is not difficult to construct an example of a computable Lebesgue-measure preserving transformation of [0, 1] and a characteristic function f = χA such that the ergodic averages Anf do not converge to a computable element of L ([0, 1]). In particular, there is no computable bo...