Unique ergodicity and random matrix products
We investigate the question: if T:X → X is a uniquely ergodic homeomorphism of a compact metrizable space and B:X → GL(k,R) is a continuous map of X into the space of invertible, k × k, real matrices does \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \...
Saved in:
| Main Author: | |
|---|---|
| Format: | Book Chapter |
| Language: | eng |
| Subjects: | |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| recordid |
cdi_springer_books_10_1007_BFb0076832 |
|---|---|
| title |
Unique ergodicity and random matrix products |
| format |
Book Chapter |
| creator |
Walters, Peter |
| subjects |
Ergodic Measure Ergodic Theorem Sphere Bundle Unique Ergodicity Vector Bundle |
| ispartof |
Lyapunov Exponents, 2006, p.37-55 |
| description |
We investigate the question: if T:X → X is a uniquely ergodic homeomorphism of a compact metrizable space and B:X → GL(k,R) is a continuous map of X into the space of invertible, k × k, real matrices does \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$\frac{1}{n}\log (||\mathop \Pi \limits_{i = 0}^{n - 1} B (T^i x)||)$$\end{document} converge uniformly to a constant? Conditions on B are given so that the answer is ‘yes’, and an example is given to show the general answer is ‘no’ when k≥2. The more general case of vector bundle automorphisms covering T is considered. |
| language |
eng |
| source |
SpringerLink Books Lecture Notes In Mathematics Archive; Springer Nature - Springer Lecture Notes in Mathematics eBooks; SpringerLINK Lecture Notes in Mathematics Archive (Through 1996) |
| identifier |
ISSN: 0075-8434 |
| fulltext |
fulltext |
| issn |
0075-8434 1617-9692 |
| url |
http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-05-21T17%3A20%3A02IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-springer&rft_val_fmt=info:ofi/fmt:kev:mtx:book&rft.genre=bookitem&rft.atitle=Unique%20ergodicity%20and%20random%20matrix%20products&rft.btitle=Lyapunov%20Exponents&rft.au=Walters,%20Peter&rft.date=2006-09-17&rft.spage=37&rft.epage=55&rft.pages=37-55&rft.issn=0075-8434&rft.eissn=1617-9692&rft.isbn=9783540164586&rft.isbn_list=3540164588&rft_id=info:doi/10.1007/BFb0076832&rft.eisbn=3540397957&rft.eisbn_list=9783540397953&rft_dat=%3Cspringer%3Espringer_books_10_1007_BFb0076832%3C/springer%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-s118t-91447e467ae21693bfb21e1ca66514393514e3bce1993d21fbb688a41ebd89a53%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_id=info:pmid/ |
| container_title |
|
| container_volume |
|
| container_issue |
|
| container_start_page |
37 |
| container_end_page |
55 |
| fullrecord |
<record><control><sourceid>springer</sourceid><recordid>TN_cdi_springer_books_10_1007_BFb0076832</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>springer_books_10_1007_BFb0076832</sourcerecordid><originalsourceid>FETCH-LOGICAL-s118t-91447e467ae21693bfb21e1ca66514393514e3bce1993d21fbb688a41ebd89a53</originalsourceid><addsrcrecordid>eNpFkDtPwzAUhc1LIi1d-AUZGQj4-vp1R6gorVSJhc6RnThVgCbFTiX496QCieV8w9E5w8fYNfA74NzcPy78CG1RnLAJKsmRDClzyjLQYArSJM7YjIw9dqClsvqcZeNEFVaivGSTlN44F0pKnrHbTdd-HkIe4rav26odvnPX1Xkco9_lOzfE9ivfx74-VEO6YheN-0hh9scp2yyeXufLYv3yvJo_rIsEYIeCQEoTpDYuCNCEvvECAlROawUSCccM6KsARFgLaLzX1joJwdeWnMIpu_n9TfvYdtsQS9_376kEXh4VlP8K8Ae3pUhj</addsrcrecordid><sourcetype>Publisher</sourcetype><isCDI>true</isCDI><recordtype>book_chapter</recordtype></control><display><type>book_chapter</type><title>Unique ergodicity and random matrix products</title><source>SpringerLink Books Lecture Notes In Mathematics Archive</source><source>Springer Nature - Springer Lecture Notes in Mathematics eBooks</source><source>SpringerLINK Lecture Notes in Mathematics Archive (Through 1996)</source><creator>Walters, Peter</creator><creatorcontrib>Walters, Peter</creatorcontrib><description>We investigate the question: if T:X → X is a uniquely ergodic homeomorphism of a compact metrizable space and B:X → GL(k,R) is a continuous map of X into the space of invertible, k × k, real matrices does \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$\frac{1}{n}\log (||\mathop \Pi \limits_{i = 0}^{n - 1} B (T^i x)||)$$\end{document} converge uniformly to a constant? Conditions on B are given so that the answer is ‘yes’, and an example is given to show the general answer is ‘no’ when k≥2. The more general case of vector bundle automorphisms covering T is considered.</description><identifier>ISSN: 0075-8434</identifier><identifier>ISBN: 9783540164586</identifier><identifier>ISBN: 3540164588</identifier><identifier>EISSN: 1617-9692</identifier><identifier>EISBN: 3540397957</identifier><identifier>EISBN: 9783540397953</identifier><identifier>DOI: 10.1007/BFb0076832</identifier><language>eng</language><publisher>Berlin, Heidelberg: Springer Berlin Heidelberg</publisher><subject>Ergodic Measure ; Ergodic Theorem ; Sphere Bundle ; Unique Ergodicity ; Vector Bundle</subject><ispartof>Lyapunov Exponents, 2006, p.37-55</ispartof><rights>Springer-Verlag 1986</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><relation>Lecture Notes in Mathematics</relation></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/BFb0076832$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/BFb0076832$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>786,787,791,800,27986,37733,38108,40926,41298,41995,42367</link.rule.ids></links><search><creatorcontrib>Walters, Peter</creatorcontrib><title>Unique ergodicity and random matrix products</title><title>Lyapunov Exponents</title><description>We investigate the question: if T:X → X is a uniquely ergodic homeomorphism of a compact metrizable space and B:X → GL(k,R) is a continuous map of X into the space of invertible, k × k, real matrices does \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$\frac{1}{n}\log (||\mathop \Pi \limits_{i = 0}^{n - 1} B (T^i x)||)$$\end{document} converge uniformly to a constant? Conditions on B are given so that the answer is ‘yes’, and an example is given to show the general answer is ‘no’ when k≥2. The more general case of vector bundle automorphisms covering T is considered.</description><subject>Ergodic Measure</subject><subject>Ergodic Theorem</subject><subject>Sphere Bundle</subject><subject>Unique Ergodicity</subject><subject>Vector Bundle</subject><issn>0075-8434</issn><issn>1617-9692</issn><isbn>9783540164586</isbn><isbn>3540164588</isbn><isbn>3540397957</isbn><isbn>9783540397953</isbn><fulltext>true</fulltext><rsrctype>book_chapter</rsrctype><creationdate>2006</creationdate><recordtype>book_chapter</recordtype><sourceid/><recordid>eNpFkDtPwzAUhc1LIi1d-AUZGQj4-vp1R6gorVSJhc6RnThVgCbFTiX496QCieV8w9E5w8fYNfA74NzcPy78CG1RnLAJKsmRDClzyjLQYArSJM7YjIw9dqClsvqcZeNEFVaivGSTlN44F0pKnrHbTdd-HkIe4rav26odvnPX1Xkco9_lOzfE9ivfx74-VEO6YheN-0hh9scp2yyeXufLYv3yvJo_rIsEYIeCQEoTpDYuCNCEvvECAlROawUSCccM6KsARFgLaLzX1joJwdeWnMIpu_n9TfvYdtsQS9_376kEXh4VlP8K8Ae3pUhj</recordid><startdate>20060917</startdate><enddate>20060917</enddate><creator>Walters, Peter</creator><general>Springer Berlin Heidelberg</general><scope/></search><sort><creationdate>20060917</creationdate><title>Unique ergodicity and random matrix products</title><author>Walters, Peter</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-s118t-91447e467ae21693bfb21e1ca66514393514e3bce1993d21fbb688a41ebd89a53</frbrgroupid><rsrctype>book_chapters</rsrctype><prefilter>book_chapters</prefilter><language>eng</language><creationdate>2006</creationdate><topic>Ergodic Measure</topic><topic>Ergodic Theorem</topic><topic>Sphere Bundle</topic><topic>Unique Ergodicity</topic><topic>Vector Bundle</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Walters, Peter</creatorcontrib></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Walters, Peter</au><format>book</format><genre>bookitem</genre><ristype>CHAP</ristype><atitle>Unique ergodicity and random matrix products</atitle><btitle>Lyapunov Exponents</btitle><seriestitle>Lecture Notes in Mathematics</seriestitle><date>2006-09-17</date><risdate>2006</risdate><spage>37</spage><epage>55</epage><pages>37-55</pages><issn>0075-8434</issn><eissn>1617-9692</eissn><isbn>9783540164586</isbn><isbn>3540164588</isbn><eisbn>3540397957</eisbn><eisbn>9783540397953</eisbn><abstract>We investigate the question: if T:X → X is a uniquely ergodic homeomorphism of a compact metrizable space and B:X → GL(k,R) is a continuous map of X into the space of invertible, k × k, real matrices does \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$\frac{1}{n}\log (||\mathop \Pi \limits_{i = 0}^{n - 1} B (T^i x)||)$$\end{document} converge uniformly to a constant? Conditions on B are given so that the answer is ‘yes’, and an example is given to show the general answer is ‘no’ when k≥2. The more general case of vector bundle automorphisms covering T is considered.</abstract><cop>Berlin, Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/BFb0076832</doi></addata></record> |