It is well known that if $f$ is a Holder continuous function from a mixing shift of finite type $X$ to $\\mathbb R$, then there exists a unique equilibrium state which is an invariant Gibbs measure having $f$ as a potential function. This result has been generalized to wider classes, such as when $X$ is a subshift with the specification property and $f$ is a function in the Bowen class. Recently Baker and Ghenciu showed that there exists a (non-invariant) Gibbs measures for the zero potential if and only if $X$ is (right-)balanced. We extend this result and show that a necessary and sufficient condition for the existence of invariant Gibbs measures on $X$ for the potential $0$ is the bi-balanced condition for $X$. We define a new condition, called $f$-balanced condition for the pair $(X,f)$ and present a similar result for the existence of Gibbs measure with respect to $f$. Using this result, we construct a class of shift spaces which have a Gibbs measure but do not have invariant Gibbs measures for the potential $0$, or equivalently, which are one-sided balanced but not bi-balanced, answering a question raised by Baker and Ghenciu."""@en ; edm:aggregatedCHO "https://circle.library.ubc.ca/rest/handle/2429/72246?expand=metadata"@en ; dcterms:extent "46.0 minutes"@en ; dc:format "video/mp4"@en ; skos:note ""@en, "Author affiliation: Ajou University"@en ; dcterms:spatial "Oaxaca (Mexico : State)"@en ; edm:isShownAt "10.14288/1.0385158"@en ; dcterms:language "eng"@en ; ns0:peerReviewStatus "Unreviewed"@en ; edm:provider "Vancouver : University of British Columbia Library"@en ; dcterms:publisher "Banff International Research Station for Mathematical Innovation and Discovery"@en ; dcterms:rights "Attribution-NonCommercial-NoDerivatives 4.0 International"@en ; ns0:rightsURI "http://creativecommons.org/licenses/by-nc-nd/4.0/"@en ; ns0:scholarLevel "Researcher"@en ; dcterms:isPartOf "BIRS Workshop Lecture Videos (Oaxaca (Mexico : State))"@en ; dcterms:subject "Mathematics"@en, "Dynamical Systems And Ergodic Theory, Group Theory And Generalizations, Dynamical Systems"@en ; dcterms:title "On balanced subshifts and the existence of invariant Gibbs measures"@en ; dcterms:type "Moving Image"@en ; ns0:identifierURI "http://hdl.handle.net/2429/72246"@en .