Ergodic properties of skew products in infinite measure

Ergodic Theory of Markov Chains Admitting an Infinite Invariant Measure.

Ergodic and Spectral Analysis of Certain Infinite Measure Preserving Transformations

0. Introduction. Throughout this paper T will denote a measure preserving transformation on a cr-finite infinite measure space (X, (B, m) which is point isomorphic with the Lebesgue measure space of the real line. Unless otherwise stated, T will be one-one. Equations involving functions or sets will always be interpreted modulo sets of measure zero. T is said to be ergodic if T~1E = E, ££(B, im...

A Weak Ergodic Theorem for Infinite Products of Lipschitzian Mappings

Let K be a bounded, closed, and convex subset of a Banach space. For a Lipschitzian self-mapping A of K , we denote by Lip(A) its Lipschitz constant. In this paper, we establish a convergence property of infinite products of Lipschitzian self-mappings of K . We consider the set of all sequences {At}t=1 of such selfmappings with the property limsupt→∞ Lip(At) ≤ 1. Endowing it with an appropriate...

Ergodic Properties of an Infinite One Dimensional Hard Rod System*

It is shown that an infinite one dimensional system of hard rods for which the "effective" velocities of the pulses (free velocity plus a drift term due to collisions) are bounded away from some neighborhood of 0 is Bernoulli. This generalizes a result of Sinai who showed that some hard rod systems are X-systems.

Infinite-horizon Lorentz tubes and gases: recurrence and ergodic properties

We construct classes of two-dimensional aperiodic Lorentz systems that have infinite horizon and are ‘chaotic’, in the sense that they are (Poincaré) recurrent, uniformly hyperbolic and ergodic, and the first-return map to any scatterer is K-mixing. In the case of the Lorentz tubes (i.e., Lorentz gases in a strip), we define general measured families of systems (ensembles) for which the above p...