{"Affiliation":[{"label":"Affiliation","value":"Non UBC","attrs":{"lang":"en","ns":"http:\/\/vivoweb.org\/ontology\/core#departmentOrSchool","classmap":"vivo:EducationalProcess","property":"vivo:departmentOrSchool"},"iri":"http:\/\/vivoweb.org\/ontology\/core#departmentOrSchool","explain":"VIVO-ISF Ontology V1.6 Property; The department or school name within institution; Not intended to be an institution name."}],"AggregatedSourceRepository":[{"label":"AggregatedSourceRepository","value":"DSpace","attrs":{"lang":"en","ns":"http:\/\/www.europeana.eu\/schemas\/edm\/dataProvider","classmap":"ore:Aggregation","property":"edm:dataProvider"},"iri":"http:\/\/www.europeana.eu\/schemas\/edm\/dataProvider","explain":"A Europeana Data Model Property; The name or identifier of the organization who contributes data indirectly to an aggregation service (e.g. Europeana)"}],"Creator":[{"label":"Creator","value":"Barbieri, Sebasti\u00e1n","attrs":{"lang":"en","ns":"http:\/\/purl.org\/dc\/terms\/creator","classmap":"dpla:SourceResource","property":"dcterms:creator"},"iri":"http:\/\/purl.org\/dc\/terms\/creator","explain":"A Dublin Core Terms Property; An entity primarily responsible for making the resource.; Examples of a Contributor include a person, an organization, or a service."}],"DateAvailable":[{"label":"DateAvailable","value":"2019-11-10T09:41:05Z","attrs":{"lang":"en","ns":"http:\/\/purl.org\/dc\/terms\/issued","classmap":"edm:WebResource","property":"dcterms:issued"},"iri":"http:\/\/purl.org\/dc\/terms\/issued","explain":"A Dublin Core Terms Property; Date of formal issuance (e.g., publication) of the resource."}],"DateIssued":[{"label":"DateIssued","value":"2019-05-13T10:00","attrs":{"lang":"en","ns":"http:\/\/purl.org\/dc\/terms\/issued","classmap":"oc:SourceResource","property":"dcterms:issued"},"iri":"http:\/\/purl.org\/dc\/terms\/issued","explain":"A Dublin Core Terms Property; Date of formal issuance (e.g., publication) of the resource."}],"Description":[{"label":"Description","value":"
\nGiven a countable amenable group $G$ one can ask which are the real numbers that can be realized as the topological entropy of a subshift of finite type (SFT). A famous result by Hochman and Meyerovitch completely characterizes these numbers for $\\mathbb{Z}^2$. I will show that the same characterization is valid for any amenable group with decidable word problem which admits an action of $\\mathbb{Z}^2$ which is free and bounded. Using this result we can give a full characterization of the entropies of SFTs for polycyclic groups. Furthermore, the same result holds for any countable group with decidable word problem which contains the direct product of any pair of infinite, finitely generated and amenable groups. In particular, it holds for many branch groups such as the Grigorchuk group.","attrs":{"lang":"en","ns":"http:\/\/purl.org\/dc\/terms\/description","classmap":"dpla:SourceResource","property":"dcterms:description"},"iri":"http:\/\/purl.org\/dc\/terms\/description","explain":"A Dublin Core Terms Property; An account of the resource.; Description may include but is not limited to: an abstract, a table of contents, a graphical representation, or a free-text account of the resource."}],"DigitalResourceOriginalRecord":[{"label":"DigitalResourceOriginalRecord","value":"https:\/\/circle.library.ubc.ca\/rest\/handle\/2429\/72239?expand=metadata","attrs":{"lang":"en","ns":"http:\/\/www.europeana.eu\/schemas\/edm\/aggregatedCHO","classmap":"ore:Aggregation","property":"edm:aggregatedCHO"},"iri":"http:\/\/www.europeana.eu\/schemas\/edm\/aggregatedCHO","explain":"A Europeana Data Model Property; The identifier of the source object, e.g. the Mona Lisa itself. This could be a full linked open date URI or an internal identifier"}],"Extent":[{"label":"Extent","value":"46.0 minutes","attrs":{"lang":"en","ns":"http:\/\/purl.org\/dc\/terms\/extent","classmap":"dpla:SourceResource","property":"dcterms:extent"},"iri":"http:\/\/purl.org\/dc\/terms\/extent","explain":"A Dublin Core Terms Property; The size or duration of the resource."}],"FileFormat":[{"label":"FileFormat","value":"video\/mp4","attrs":{"lang":"en","ns":"http:\/\/purl.org\/dc\/elements\/1.1\/format","classmap":"edm:WebResource","property":"dc:format"},"iri":"http:\/\/purl.org\/dc\/elements\/1.1\/format","explain":"A Dublin Core Elements Property; The file format, physical medium, or dimensions of the resource.; Examples of dimensions include size and duration. Recommended best practice is to use a controlled vocabulary such as the list of Internet Media Types [MIME]."}],"FullText":[{"label":"FullText","value":"","attrs":{"lang":"en","ns":"http:\/\/www.w3.org\/2009\/08\/skos-reference\/skos.html#note","classmap":"oc:AnnotationContainer"},"iri":"http:\/\/www.w3.org\/2009\/08\/skos-reference\/skos.html#note","explain":"Simple Knowledge Organisation System; Notes are used to provide information relating to SKOS concepts. There is no restriction on the nature of this information, e.g., it could be plain text, hypertext, or an image; it could be a definition, information about the scope of a concept, editorial information, or any other type of information."}],"IsShownAt":[{"label":"IsShownAt","value":"10.14288\/1.0385151","attrs":{"lang":"en","ns":"http:\/\/www.europeana.eu\/schemas\/edm\/isShownAt","classmap":"edm:WebResource","property":"edm:isShownAt"},"iri":"http:\/\/www.europeana.eu\/schemas\/edm\/isShownAt","explain":"A Europeana Data Model Property; An unambiguous URL reference to the digital object on the provider\u2019s website in its full information context."}],"Language":[{"label":"Language","value":"eng","attrs":{"lang":"en","ns":"http:\/\/purl.org\/dc\/terms\/language","classmap":"dpla:SourceResource","property":"dcterms:language"},"iri":"http:\/\/purl.org\/dc\/terms\/language","explain":"A Dublin Core Terms Property; A language of the resource.; Recommended best practice is to use a controlled vocabulary such as RFC 4646 [RFC4646]."}],"Notes":[{"label":"Notes","value":"Author affiliation: University of British Columbia","attrs":{"lang":"en","ns":"http:\/\/www.w3.org\/2009\/08\/skos-reference\/skos.html#note","classmap":"skos:Concept","property":"skos:note"},"iri":"http:\/\/www.w3.org\/2009\/08\/skos-reference\/skos.html#note","explain":"Simple Knowledge Organisation System; Notes are used to provide information relating to SKOS concepts. There is no restriction on the nature of this information, e.g., it could be plain text, hypertext, or an image; it could be a definition, information about the scope of a concept, editorial information, or any other type of information."}],"PeerReviewStatus":[{"label":"PeerReviewStatus","value":"Unreviewed","attrs":{"lang":"en","ns":"https:\/\/open.library.ubc.ca\/terms#peerReviewStatus","classmap":"oc:PublicationDescription","property":"oc:peerReviewStatus"},"iri":"https:\/\/open.library.ubc.ca\/terms#peerReviewStatus","explain":"UBC Open Collections Metadata Components; Local Field; Identifies whether or not the resource is peer-reviewed. Applies to published resources only."}],"Provider":[{"label":"Provider","value":"Vancouver : University of British Columbia Library","attrs":{"lang":"en","ns":"http:\/\/www.europeana.eu\/schemas\/edm\/provider","classmap":"ore:Aggregation","property":"edm:provider"},"iri":"http:\/\/www.europeana.eu\/schemas\/edm\/provider","explain":"A Europeana Data Model Property; The name or identifier of the organization who delivers data directly to an aggregation service (e.g. Europeana)"}],"Publisher":[{"label":"Publisher","value":"Banff International Research Station for Mathematical Innovation and Discovery","attrs":{"lang":"en","ns":"http:\/\/purl.org\/dc\/terms\/publisher","classmap":"dpla:SourceResource","property":"dcterms:publisher"},"iri":"http:\/\/purl.org\/dc\/terms\/publisher","explain":"A Dublin Core Terms Property; An entity responsible for making the resource available.; Examples of a Publisher include a person, an organization, or a service."}],"Rights":[{"label":"Rights","value":"Attribution-NonCommercial-NoDerivatives 4.0 International","attrs":{"lang":"en","ns":"http:\/\/purl.org\/dc\/terms\/rights","classmap":"edm:WebResource","property":"dcterms:rights"},"iri":"http:\/\/purl.org\/dc\/terms\/rights","explain":"A Dublin Core Terms Property; Information about rights held in and over the resource.; Typically, rights information includes a statement about various property rights associated with the resource, including intellectual property rights."}],"RightsURI":[{"label":"RightsURI","value":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/","attrs":{"lang":"en","ns":"https:\/\/open.library.ubc.ca\/terms#rightsURI","classmap":"oc:PublicationDescription","property":"oc:rightsURI"},"iri":"https:\/\/open.library.ubc.ca\/terms#rightsURI","explain":"UBC Open Collections Metadata Components; Local Field; Indicates the Creative Commons license url."}],"ScholarlyLevel":[{"label":"ScholarlyLevel","value":"Postdoctoral","attrs":{"lang":"en","ns":"https:\/\/open.library.ubc.ca\/terms#scholarLevel","classmap":"oc:PublicationDescription","property":"oc:scholarLevel"},"iri":"https:\/\/open.library.ubc.ca\/terms#scholarLevel","explain":"UBC Open Collections Metadata Components; Local Field; Identifies the scholarly level of the author(s)\/creator(s)."}],"Series":[{"label":"Series","value":"BIRS Workshop Lecture Videos (Oaxaca de Ju\u00e1rez (Mexico))","attrs":{"lang":"en","ns":"http:\/\/purl.org\/dc\/terms\/isPartOf","classmap":"oc:PublicationDescription","property":"dcterms:isPartOf"},"iri":"http:\/\/purl.org\/dc\/terms\/isPartOf","explain":"A Dublin Core Terms Property; A related resource in which the described resource is physically or logically included."}],"Subject":[{"label":"Subject","value":"Mathematics","attrs":{"lang":"en","ns":"http:\/\/purl.org\/dc\/terms\/subject","classmap":"dpla:SourceResource","property":"dcterms:subject"},"iri":"http:\/\/purl.org\/dc\/terms\/subject","explain":"A Dublin Core Terms Property; The topic of the resource.; Typically, the subject will be represented using keywords, key phrases, or classification codes. Recommended best practice is to use a controlled vocabulary."},{"label":"Subject","value":"Dynamical systems and ergodic theory","attrs":{"lang":"en","ns":"http:\/\/purl.org\/dc\/terms\/subject","classmap":"dpla:SourceResource","property":"dcterms:subject"},"iri":"http:\/\/purl.org\/dc\/terms\/subject","explain":"A Dublin Core Terms Property; The topic of the resource.; Typically, the subject will be represented using keywords, key phrases, or classification codes. Recommended best practice is to use a controlled vocabulary."},{"label":"Subject","value":"Group theory and generalizations","attrs":{"lang":"en","ns":"http:\/\/purl.org\/dc\/terms\/subject","classmap":"dpla:SourceResource","property":"dcterms:subject"},"iri":"http:\/\/purl.org\/dc\/terms\/subject","explain":"A Dublin Core Terms Property; The topic of the resource.; Typically, the subject will be represented using keywords, key phrases, or classification codes. Recommended best practice is to use a controlled vocabulary."},{"label":"Subject","value":"Dynamical systems","attrs":{"lang":"en","ns":"http:\/\/purl.org\/dc\/terms\/subject","classmap":"dpla:SourceResource","property":"dcterms:subject"},"iri":"http:\/\/purl.org\/dc\/terms\/subject","explain":"A Dublin Core Terms Property; The topic of the resource.; Typically, the subject will be represented using keywords, key phrases, or classification codes. Recommended best practice is to use a controlled vocabulary."}],"Title":[{"label":"Title","value":"Topological entropies of SFTs in amenable groups","attrs":{"lang":"en","ns":"http:\/\/purl.org\/dc\/terms\/title","classmap":"dpla:SourceResource","property":"dcterms:title"},"iri":"http:\/\/purl.org\/dc\/terms\/title","explain":"A Dublin Core Terms Property; The name given to the resource."}],"Type":[{"label":"Type","value":"Moving Image","attrs":{"lang":"en","ns":"http:\/\/purl.org\/dc\/terms\/type","classmap":"dpla:SourceResource","property":"dcterms:type"},"iri":"http:\/\/purl.org\/dc\/terms\/type","explain":"A Dublin Core Terms Property; The nature or genre of the resource.; Recommended best practice is to use a controlled vocabulary such as the DCMI Type Vocabulary [DCMITYPE]. To describe the file format, physical medium, or dimensions of the resource, use the Format element."}],"URI":[{"label":"URI","value":"http:\/\/hdl.handle.net\/2429\/72239","attrs":{"lang":"en","ns":"https:\/\/open.library.ubc.ca\/terms#identifierURI","classmap":"oc:PublicationDescription","property":"oc:identifierURI"},"iri":"https:\/\/open.library.ubc.ca\/terms#identifierURI","explain":"UBC Open Collections Metadata Components; Local Field; Indicates the handle for item record."}],"SortDate":[{"label":"Sort Date","value":"2019-05-13 AD","attrs":{"lang":"en","ns":"http:\/\/purl.org\/dc\/terms\/date","classmap":"oc:InternalResource","property":"dcterms:date"},"iri":"http:\/\/purl.org\/dc\/terms\/date","explain":"A Dublin Core Elements Property; A point or period of time associated with an event in the lifecycle of the resource.; Date may be used to express temporal information at any level of granularity. Recommended best practice is to use an encoding scheme, such as the W3CDTF profile of ISO 8601 [W3CDTF].; A point or period of time associated with an event in the lifecycle of the resource.; Date may be used to express temporal information at any level of granularity. Recommended best practice is to use an encoding scheme, such as the W3CDTF profile of ISO 8601 [W3CDTF]."}]}