Notes on Ergodic Theory in Infinite Measure Spaces

Notes on Ergodic Theory in Infinite Measure Spaces

Show other versions (2)

This article is concerned with ergodic theory for transformations which preserve an infinite measure. In the first part we present an overview of the invertible case with a focus on weakly wandering sequences and their applications to number theory as it has developed over the last fifty years. The...

Full description

Bibliographic Details
Main Authors: Victor Arzumanian, Stanley Eigen, Arshag Hajian
Format: Article
Language:English
Published: Republic of Armenia National Academy of Sciences 2015-12-01
Series:Armenian Journal of Mathematics
Online Access:http://www.armjmath.sci.am/index.php/ajm/article/view/115
id doaj-cd0d72fe37954d43832d2048be19bfef
record_format Article
spelling doaj-cd0d72fe37954d43832d2048be19bfef2020-11-24T21:05:51ZengRepublic of Armenia National Academy of SciencesArmenian Journal of Mathematics1829-11632015-12-0172Notes on Ergodic Theory in Infinite Measure SpacesVictor Arzumanian0Stanley Eigen1Arshag Hajian2Institute of Mathematics, NAS of Armenia, 24/5 Baghramian Ave., Yerevan, 0019, ArmeniaNortheastern University 360 Huntington Avenue, Boston, MA, 02115 USANortheastern University 360 Huntington Avenue, Boston, MA, 02115 USA This article is concerned with ergodic theory for transformations which preserve an infinite measure. In the first part we present an overview of the invertible case with a focus on weakly wandering sequences and their applications to number theory as it has developed over the last fifty years. The second part presents a very preliminary investigation into extending weakly wandering sequences to the non-invertible case. This consists primarily of a few examples which illustrate the complexities which arise in the non-invertible case. http://www.armjmath.sci.am/index.php/ajm/article/view/115
collection DOAJ
language English
format Article
sources DOAJ
author Victor Arzumanian
Stanley Eigen
Arshag Hajian
spellingShingle Victor Arzumanian
Stanley Eigen
Arshag Hajian
Notes on Ergodic Theory in Infinite Measure Spaces
Armenian Journal of Mathematics
author_facet Victor Arzumanian
Stanley Eigen
Arshag Hajian
author_sort Victor Arzumanian
title Notes on Ergodic Theory in Infinite Measure Spaces
title_short Notes on Ergodic Theory in Infinite Measure Spaces
title_full Notes on Ergodic Theory in Infinite Measure Spaces
title_fullStr Notes on Ergodic Theory in Infinite Measure Spaces
title_full_unstemmed Notes on Ergodic Theory in Infinite Measure Spaces
title_sort notes on ergodic theory in infinite measure spaces
publisher Republic of Armenia National Academy of Sciences
series Armenian Journal of Mathematics
issn 1829-1163
publishDate 2015-12-01
description This article is concerned with ergodic theory for transformations which preserve an infinite measure. In the first part we present an overview of the invertible case with a focus on weakly wandering sequences and their applications to number theory as it has developed over the last fifty years. The second part presents a very preliminary investigation into extending weakly wandering sequences to the non-invertible case. This consists primarily of a few examples which illustrate the complexities which arise in the non-invertible case.
url http://www.armjmath.sci.am/index.php/ajm/article/view/115
work_keys_str_mv AT victorarzumanian notesonergodictheoryininfinitemeasurespaces
AT stanleyeigen notesonergodictheoryininfinitemeasurespaces
AT arshaghajian notesonergodictheoryininfinitemeasurespaces
_version_ 1716767656383610880

Similar Items