Mixing constructions with infinite invariant measure and spectral multiplicities

We introduce high staircase infinite measure preserving transformations and prove that they are mixing under a restricted growth condition. This is used to (i) realize each subset $M\subset \Bbb N\cup \{\infty \}$ as the set of essential values of the multiplicity function for the Koopman operator o...

Full description

Saved in:
Bibliographic Details
Published in:Ergodic theory and dynamical systems 2011-06, Vol.31 (3), p.853-873
Main Authors: DANILENKO, ALEXANDRE I., RYZHIKOV, VALERY V.
Format: Article
Language:English
Subjects:
Automorphisms
Construction
Dynamical systems
Ergodic processes
Invariants
Preserving
Spectra
Spectrum analysis
Transformations
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by cdi_FETCH-LOGICAL-c392t-7e53d1e38e364f2ebbf1354cb501f71550aa8acc827b51180ad1cb071679f1413
cites cdi_FETCH-LOGICAL-c392t-7e53d1e38e364f2ebbf1354cb501f71550aa8acc827b51180ad1cb071679f1413
container_end_page 873
container_issue 3
container_start_page 853
container_title Ergodic theory and dynamical systems
container_volume 31
creator DANILENKO, ALEXANDRE I.
RYZHIKOV, VALERY V.
description We introduce high staircase infinite measure preserving transformations and prove that they are mixing under a restricted growth condition. This is used to (i) realize each subset $M\subset \Bbb N\cup \{\infty \}$ as the set of essential values of the multiplicity function for the Koopman operator of a mixing ergodic infinite measure preserving transformation, (ii) construct mixing power weakly mixing infinite measure preserving transformations, and (iii) construct mixing Poissonian automorphisms with a simple spectrum, etc.
doi_str_mv 10.1017/S0143385710000052
format article
fullrecord <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_1541431652</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><cupid>10_1017_S0143385710000052</cupid><sourcerecordid>1541431652</sourcerecordid><originalsourceid>FETCH-LOGICAL-c392t-7e53d1e38e364f2ebbf1354cb501f71550aa8acc827b51180ad1cb071679f1413</originalsourceid><addsrcrecordid>eNp1kE9LxDAQxYMouK5-AG_Fk5dqpkma9iiLrsKKgnouaTpds7RpTVL_fHtbdkFQnMs8mN97zAwhp0AvgIK8fKLAGcuEBDqVSPbIDHiax5yD3CezaRxP80Ny5P1mRBhIMSOP9-bT2HWkO-uDG3Qwo4g-THiNjK2NNQFH8a6cUTZELSo_OIyUrSLfow5ONVE7NMH0jdEmGPTH5KBWjceTXZ-Tl5vr58VtvHpY3i2uVrFmeRJiiYJVgCxDlvI6wbKsgQmuS0GhliAEVSpTWmeJLAVARlUFuqQSUpnXwIHNyfk2t3fd24A-FK3xGptGWewGX4Dg48mQimREz36hm25wdtyuyFKRQ5rmEwRbSLvOe4d10TvTKvdVAC2mFxd_Xjx62M6j2tKZao0_yf-7vgGy9n2v</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>865916692</pqid></control><display><type>article</type><title>Mixing constructions with infinite invariant measure and spectral multiplicities</title><source>Cambridge Journals Online</source><creator>DANILENKO, ALEXANDRE I. ; RYZHIKOV, VALERY V.</creator><creatorcontrib>DANILENKO, ALEXANDRE I. ; RYZHIKOV, VALERY V.</creatorcontrib><description>We introduce high staircase infinite measure preserving transformations and prove that they are mixing under a restricted growth condition. This is used to (i) realize each subset $M\subset \Bbb N\cup \{\infty \}$ as the set of essential values of the multiplicity function for the Koopman operator of a mixing ergodic infinite measure preserving transformation, (ii) construct mixing power weakly mixing infinite measure preserving transformations, and (iii) construct mixing Poissonian automorphisms with a simple spectrum, etc.</description><identifier>ISSN: 0143-3857</identifier><identifier>EISSN: 1469-4417</identifier><identifier>DOI: 10.1017/S0143385710000052</identifier><language>eng</language><publisher>Cambridge, UK: Cambridge University Press</publisher><subject>Automorphisms ; Construction ; Dynamical systems ; Ergodic processes ; Invariants ; Preserving ; Spectra ; Spectrum analysis ; Transformations</subject><ispartof>Ergodic theory and dynamical systems, 2011-06, Vol.31 (3), p.853-873</ispartof><rights>Copyright © Cambridge University Press 2010</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c392t-7e53d1e38e364f2ebbf1354cb501f71550aa8acc827b51180ad1cb071679f1413</citedby><cites>FETCH-LOGICAL-c392t-7e53d1e38e364f2ebbf1354cb501f71550aa8acc827b51180ad1cb071679f1413</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.cambridge.org/core/product/identifier/S0143385710000052/type/journal_article$$EHTML$$P50$$Gcambridge$$H</linktohtml><link.rule.ids>314,780,784,27923,27924,72831</link.rule.ids></links><search><creatorcontrib>DANILENKO, ALEXANDRE I.</creatorcontrib><creatorcontrib>RYZHIKOV, VALERY V.</creatorcontrib><title>Mixing constructions with infinite invariant measure and spectral multiplicities</title><title>Ergodic theory and dynamical systems</title><addtitle>Ergod. Th. Dynam. Sys</addtitle><description>We introduce high staircase infinite measure preserving transformations and prove that they are mixing under a restricted growth condition. This is used to (i) realize each subset $M\subset \Bbb N\cup \{\infty \}$ as the set of essential values of the multiplicity function for the Koopman operator of a mixing ergodic infinite measure preserving transformation, (ii) construct mixing power weakly mixing infinite measure preserving transformations, and (iii) construct mixing Poissonian automorphisms with a simple spectrum, etc.</description><subject>Automorphisms</subject><subject>Construction</subject><subject>Dynamical systems</subject><subject>Ergodic processes</subject><subject>Invariants</subject><subject>Preserving</subject><subject>Spectra</subject><subject>Spectrum analysis</subject><subject>Transformations</subject><issn>0143-3857</issn><issn>1469-4417</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2011</creationdate><recordtype>article</recordtype><recordid>eNp1kE9LxDAQxYMouK5-AG_Fk5dqpkma9iiLrsKKgnouaTpds7RpTVL_fHtbdkFQnMs8mN97zAwhp0AvgIK8fKLAGcuEBDqVSPbIDHiax5yD3CezaRxP80Ny5P1mRBhIMSOP9-bT2HWkO-uDG3Qwo4g-THiNjK2NNQFH8a6cUTZELSo_OIyUrSLfow5ONVE7NMH0jdEmGPTH5KBWjceTXZ-Tl5vr58VtvHpY3i2uVrFmeRJiiYJVgCxDlvI6wbKsgQmuS0GhliAEVSpTWmeJLAVARlUFuqQSUpnXwIHNyfk2t3fd24A-FK3xGptGWewGX4Dg48mQimREz36hm25wdtyuyFKRQ5rmEwRbSLvOe4d10TvTKvdVAC2mFxd_Xjx62M6j2tKZao0_yf-7vgGy9n2v</recordid><startdate>201106</startdate><enddate>201106</enddate><creator>DANILENKO, ALEXANDRE I.</creator><creator>RYZHIKOV, VALERY V.</creator><general>Cambridge University Press</general><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7SC</scope><scope>7U5</scope><scope>7XB</scope><scope>88I</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>GNUQQ</scope><scope>H8D</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>L6V</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>M2P</scope><scope>M7S</scope><scope>P5Z</scope><scope>P62</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>Q9U</scope></search><sort><creationdate>201106</creationdate><title>Mixing constructions with infinite invariant measure and spectral multiplicities</title><author>DANILENKO, ALEXANDRE I. ; RYZHIKOV, VALERY V.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c392t-7e53d1e38e364f2ebbf1354cb501f71550aa8acc827b51180ad1cb071679f1413</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2011</creationdate><topic>Automorphisms</topic><topic>Construction</topic><topic>Dynamical systems</topic><topic>Ergodic processes</topic><topic>Invariants</topic><topic>Preserving</topic><topic>Spectra</topic><topic>Spectrum analysis</topic><topic>Transformations</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>DANILENKO, ALEXANDRE I.</creatorcontrib><creatorcontrib>RYZHIKOV, VALERY V.</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>Computer and Information Systems Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>Science Database (Alumni Edition)</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>Materials Science &amp; Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central</collection><collection>Advanced Technologies &amp; Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central</collection><collection>ProQuest Central Student</collection><collection>Aerospace Database</collection><collection>SciTech Premium Collection (Proquest) (PQ_SDU_P3)</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer Science Database</collection><collection>ProQuest Engineering Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts – Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>ProQuest Science Journals</collection><collection>Engineering Database</collection><collection>Advanced Technologies &amp; Aerospace Database</collection><collection>ProQuest Advanced Technologies &amp; Aerospace Collection</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection><collection>ProQuest Central Basic</collection><jtitle>Ergodic theory and dynamical systems</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>DANILENKO, ALEXANDRE I.</au><au>RYZHIKOV, VALERY V.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Mixing constructions with infinite invariant measure and spectral multiplicities</atitle><jtitle>Ergodic theory and dynamical systems</jtitle><addtitle>Ergod. Th. Dynam. Sys</addtitle><date>2011-06</date><risdate>2011</risdate><volume>31</volume><issue>3</issue><spage>853</spage><epage>873</epage><pages>853-873</pages><issn>0143-3857</issn><eissn>1469-4417</eissn><abstract>We introduce high staircase infinite measure preserving transformations and prove that they are mixing under a restricted growth condition. This is used to (i) realize each subset $M\subset \Bbb N\cup \{\infty \}$ as the set of essential values of the multiplicity function for the Koopman operator of a mixing ergodic infinite measure preserving transformation, (ii) construct mixing power weakly mixing infinite measure preserving transformations, and (iii) construct mixing Poissonian automorphisms with a simple spectrum, etc.</abstract><cop>Cambridge, UK</cop><pub>Cambridge University Press</pub><doi>10.1017/S0143385710000052</doi><tpages>21</tpages><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 0143-3857
ispartof Ergodic theory and dynamical systems, 2011-06, Vol.31 (3), p.853-873
issn 0143-3857
1469-4417
language eng
recordid cdi_proquest_miscellaneous_1541431652
source Cambridge Journals Online
subjects Automorphisms
Construction
Dynamical systems
Ergodic processes
Invariants
Preserving
Spectra
Spectrum analysis
Transformations
title Mixing constructions with infinite invariant measure and spectral multiplicities
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-08T07%3A53%3A34IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Mixing%20constructions%20with%20infinite%20invariant%20measure%20and%20spectral%20multiplicities&rft.jtitle=Ergodic%20theory%20and%20dynamical%20systems&rft.au=DANILENKO,%20ALEXANDRE%20I.&rft.date=2011-06&rft.volume=31&rft.issue=3&rft.spage=853&rft.epage=873&rft.pages=853-873&rft.issn=0143-3857&rft.eissn=1469-4417&rft_id=info:doi/10.1017/S0143385710000052&rft_dat=%3Cproquest_cross%3E1541431652%3C/proquest_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c392t-7e53d1e38e364f2ebbf1354cb501f71550aa8acc827b51180ad1cb071679f1413%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=865916692&rft_id=info:pmid/&rft_cupid=10_1017_S0143385710000052&rfr_iscdi=true