scholarly journals Time change and orbit equivalence in ergodic theory

1988 ◽  
Vol 18 (2) ◽  
pp. 399-412 ◽  
Author(s):  
Munetaka Nakamura
ISRN Algebra ◽  
2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Samuel Coskey

We give a survey of Adrian Ioana's cocycle superrigidity theorem for profinite actions of Property (T) groups and its applications to ergodic theory and set theory in this expository paper. In addition to a statement and proof of Ioana's theorem, this paper features the following: (i) an introduction to rigidity, including a crash course in Borel cocycles and a summary of some of the best-known superrigidity theorems; (ii) some easy applications of superrigidity, both to ergodic theory (orbit equivalence) and set theory (Borel reducibility); and (iii) a streamlined proof of Simon Thomas's theorem that the classification of torsion-free abelian groups of finite rank is intractable.


Author(s):  
Karl E. Petersen
Keyword(s):  

1995 ◽  
Vol 31 (7) ◽  
pp. 51-59 ◽  
Author(s):  
Ian Guymer ◽  
Rob O'Brien

Previously, the design of sewer systems has been limited to studies of their hydraulic characteristics, in particular the ability of the system to convey the maximum discharge. Greater environmental awareness has necessitated that new designs, and some existing schemes, are assessed to determine the environmental load which the scheme will deliver to any downstream component. This paper describes a laboratory programme which has been designed to elucidate the effects of manholes on the longitudinal dispersion of solutes. A laboratory system is described, which allows in situ measurements to be taken of the concentration of a fluorescent solute tracer, both up- and down-stream of a surcharged manhole junction. Results are presented from a preliminary series of studies undertaken for a single manhole geometry over a range of discharges, with varying levels of surcharge. Results are presented showing the variation of travel time, change in second moment of the distribution and of a dispersion factor with surcharge, assuming a Taylor approach and determining the dispersion factor using a ‘change in moment’ method. The effect of the stored volume within the manhole is clearly evident. The limitations and the applicability of this approach are discussed.


2020 ◽  
pp. 1-15
Author(s):  
ALEXANDER S. KECHRIS ◽  
MACIEJ MALICKI ◽  
ARISTOTELIS PANAGIOTOPOULOS ◽  
JOSEPH ZIELINSKI

Abstract It is a long-standing open question whether every Polish group that is not locally compact admits a Borel action on a standard Borel space whose associated orbit equivalence relation is not essentially countable. We answer this question positively for the class of all Polish groups that embed in the isometry group of a locally compact metric space. This class contains all non-archimedean Polish groups, for which we provide an alternative proof based on a new criterion for non-essential countability. Finally, we provide the following variant of a theorem of Solecki: every infinite-dimensional Banach space has a continuous action whose orbit equivalence relation is Borel but not essentially countable.


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