Finite ergodic index and asymmetry for infinite measure preserving actions

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...

DIRECTIONAL RECURRENCE FOR INFINITE MEASURE PRESERVING Zd ACTIONS

We define directional recurrence for infinite measure preserving Z actions both intrinsically and via the unit suspension flow and prove that the two definitions are equivalent. We study the structure of the set of recurrent directions and show it is always a Gδ set. We construct an example of a recurrent action with no recurrent directions, answering a question posed in a 2007 paper of Daniel ...

Poisson-Pinsker factor and infinite measure preserving group actions

We solve the question of the existence of a Poisson-Pinsker factor for conservative ergodic infinite measure preserving action of a countable amenable group by proving the following dichotomy: either it has totally positive Poisson entropy (and is of zero type), or it possesses a Poisson-Pinsker factor. If G is abelian and the entropy positive, the spectrum is absolutely continuous (Lebesgue co...

Quasi-factors for Infinite-measure Preserving Transformations

This paper is a study of Glasner’s definition of quasi-factors in the setting of infinite-measure preserving system. The existence of a system with zero Krengel entropy and a quasi-factor with positive entropy is obtained. On the other hand, relative zero-entropy for conservative systems implies relative zero-entropy of any quasi-factor with respect to its natural projection onto the factor. Th...

Infinite Measure Preserving Transformations with "mixing"