{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,21]],"date-time":"2026-02-21T07:30:00Z","timestamp":1771659000616,"version":"3.50.1"},"reference-count":30,"publisher":"IOP Publishing","issue":"12","license":[{"start":{"date-parts":[[2021,11,11]],"date-time":"2021-11-11T00:00:00Z","timestamp":1636588800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/publishingsupport.iopscience.iop.org\/iop-standard\/v1"},{"start":{"date-parts":[[2021,11,11]],"date-time":"2021-11-11T00:00:00Z","timestamp":1636588800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/iopscience.iop.org\/info\/page\/text-and-data-mining"}],"content-domain":{"domain":["iopscience.iop.org"],"crossmark-restriction":false},"short-container-title":["Nonlinearity"],"published-print":{"date-parts":[[2021,12,1]]},"abstract":"Abstract<\/jats:title>\n \n We show the existence of invariant ergodic\n \u03c3<\/jats:italic>\n -additive probability measures with full support on\n X<\/jats:italic>\n for a class of linear operators\n L<\/jats:italic>\n :\n X<\/jats:italic>\n \u2192\n X<\/jats:italic>\n , where\n L<\/jats:italic>\n is a weighted shift operator and\n X<\/jats:italic>\n either is the Banach space\n \n \n \n <\/jats:tex-math>\n \n \n \n c<\/mml:mi>\n <\/mml:mrow>\n \n 0<\/mml:mn>\n <\/mml:mrow>\n <\/mml:msub>\n \n (<\/mml:mo>\n \n R<\/mml:mi>\n <\/mml:mrow>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n or\n \n \n \n <\/jats:tex-math>\n \n \n \n l<\/mml:mi>\n <\/mml:mrow>\n \n p<\/mml:mi>\n <\/mml:mrow>\n <\/mml:msup>\n \n (<\/mml:mo>\n \n R<\/mml:mi>\n <\/mml:mrow>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n for 1 \u2a7d\n p<\/jats:italic>\n < \u221e. In order to do so, we adapt ideas from thermodynamic formalism as follows. For a given bounded H\u00f6lder continuous potential\n \n \n \n <\/jats:tex-math>\n \n A<\/mml:mi>\n :<\/mml:mo>\n X<\/mml:mi>\n \u2192<\/mml:mo>\n R<\/mml:mi>\n <\/mml:math>\n <\/jats:inline-formula>\n , we define a transfer operator\n \n \n \n <\/jats:tex-math>\n \n \n \n L<\/mml:mi>\n <\/mml:mrow>\n \n A<\/mml:mi>\n <\/mml:mrow>\n <\/mml:msub>\n <\/mml:math>\n <\/jats:inline-formula>\n which acts on continuous functions on\n X<\/jats:italic>\n and prove that this operator satisfies a Ruelle\u2013Perron\u2013Frobenius theorem. That is, we show the existence of an eigenfunction for\n \n \n \n <\/jats:tex-math>\n \n \n \n L<\/mml:mi>\n <\/mml:mrow>\n \n A<\/mml:mi>\n <\/mml:mrow>\n <\/mml:msub>\n <\/mml:math>\n <\/jats:inline-formula>\n which provides us with a normalised potential\n \n \n \n <\/jats:tex-math>\n \n \n \n \n A<\/mml:mi>\n <\/mml:mrow>\n \u00af<\/mml:mo>\n <\/mml:mover>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n and an action of the dual operator\n \n \n \n <\/jats:tex-math>\n \n \n \n L<\/mml:mi>\n <\/mml:mrow>\n \n \n \n A<\/mml:mi>\n <\/mml:mrow>\n \u00af<\/mml:mo>\n <\/mml:mover>\n <\/mml:mrow>\n \n *<\/mml:mo>\n <\/mml:mrow>\n <\/mml:msubsup>\n <\/mml:math>\n <\/jats:inline-formula>\n on the one-Wasserstein space of probabilities on\n X<\/jats:italic>\n with a unique fixed point, to which we refer to as Gibbs probability. It is worth noting that the definition of\n \n \n \n <\/jats:tex-math>\n \n \n \n L<\/mml:mi>\n <\/mml:mrow>\n \n A<\/mml:mi>\n <\/mml:mrow>\n <\/mml:msub>\n <\/mml:math>\n <\/jats:inline-formula>\n requires an\n a priori<\/jats:italic>\n probability on the kernel of\n L<\/jats:italic>\n . These results are extended to a wide class of operators with a non-trivial kernel defined on separable Banach spaces.\n <\/jats:p>","DOI":"10.1088\/1361-6544\/ac3382","type":"journal-article","created":{"date-parts":[[2021,11,11]],"date-time":"2021-11-11T04:43:54Z","timestamp":1636605834000},"page":"8359-8391","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":3,"title":["Invariant probabilities for discrete time linear dynamics via thermodynamic formalism\n *<\/sup>"],"prefix":"10.1088","volume":"34","author":[{"given":"Artur O","family":"Lopes","sequence":"first","affiliation":[]},{"given":"Ali","family":"Messaoudi","sequence":"additional","affiliation":[]},{"given":"Manuel","family":"Stadlbauer","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2785-6576","authenticated-orcid":false,"given":"Victor","family":"Vargas","sequence":"additional","affiliation":[]}],"member":"266","published-online":{"date-parts":[[2021,11,11]]},"reference":[{"key":"nonac3382bib1","doi-asserted-by":"publisher","first-page":"2506","DOI":"10.1002\/mana.201700229","type":"journal-article","article-title":"A variational principle for the specific entropy for symbolic systems with uncountable alphabets","volume":"291","author":"Aguiar","year":"2018","journal-title":"Math. 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All rights, including for text and data mining, AI training, and similar technologies, are reserved.","name":"copyright_information","label":"Copyright Information"},{"value":"2020-06-22","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2021-10-26","name":"date_accepted","label":"Date Accepted","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2021-11-11","name":"date_epub","label":"Online publication date","group":{"name":"publication_dates","label":"Publication dates"}}]}}