{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,4]],"date-time":"2025-11-04T13:18:32Z","timestamp":1762262312068,"version":"build-2065373602"},"reference-count":0,"publisher":"European Mathematical Society - EMS - Publishing House GmbH","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Rev. Mat. Iberoam."],"published-print":{"date-parts":[[2020,1,3]]},"abstract":"<jats:p>\n                    We study the cohomological equation associated to linear cocycles on semi simple Lie groups\n                    <jats:inline-formula>\n                      <jats:tex-math>\\mathcal G<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    over hyperbolic dynamics. We give sufficient conditions for the solution of the cohomological equation of fiber-bunched cocycles to be unique and for the H\u00f6lder conjugacy class of the cocycle to coincide with\n                    <jats:inline-formula>\n                      <jats:tex-math>C^\\nu(M,\\mathcal G)<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    . In particular, we prove that there exists an open and dense subset of the set\n                    <jats:inline-formula>\n                      <jats:tex-math>C_b^\\nu(M,\\mathcal G)<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    of fiber-bunched cocycles with trivial centralizer. As a consequence we deduce that the solutions of the {cohomological} equation of fiber-bunched cocycles form a finite abelian subgroup of\n                    <jats:inline-formula>\n                      <jats:tex-math>C_b^\\nu(M,\\mathcal G)<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    for an open and dense subset of fiber-bunched cocycles in\n                    <jats:inline-formula>\n                      <jats:tex-math>C_b^\\nu(M,\\mathcal G)<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    . Some results on the centralizer of skew-products are also given.\n                  <\/jats:p>","DOI":"10.4171\/rmi\/1160","type":"journal-article","created":{"date-parts":[[2020,1,3]],"date-time":"2020-01-03T17:30:16Z","timestamp":1578072616000},"page":"1113-1132","source":"Crossref","is-referenced-by-count":1,"title":["On the cohomology class of fiber-bunched cocycles on semi simple Lie groups"],"prefix":"10.4171","volume":"36","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0902-8718","authenticated-orcid":false,"given":"Paulo","family":"Varandas","sequence":"first","affiliation":[{"name":"Universidade Federal da Bahia, Salvador, Brazil and Universidade do Porto, Portugal"}]}],"member":"2673","container-title":["Revista Matem\u00e1tica Iberoamericana"],"original-title":[],"link":[{"URL":"https:\/\/www.ems-ph.org\/fulltext\/10.4171\/rmi\/1160","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,4]],"date-time":"2025-11-04T13:09:18Z","timestamp":1762261758000},"score":1,"resource":{"primary":{"URL":"https:\/\/ems.press\/doi\/10.4171\/rmi\/1160"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,1,3]]},"references-count":0,"journal-issue":{"issue":"4"},"URL":"https:\/\/doi.org\/10.4171\/rmi\/1160","relation":{},"ISSN":["0213-2230","2235-0616"],"issn-type":[{"type":"print","value":"0213-2230"},{"type":"electronic","value":"2235-0616"}],"subject":[],"published":{"date-parts":[[2020,1,3]]}}}