{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T12:31:34Z","timestamp":1787229094694,"version":"build-2736575974"},"reference-count":21,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Appl. Dyn. Syst."],"published-print":{"date-parts":[[2012,1]]},"abstract":"<jats:p>For the subshift of finite type $\\Sigma=\\{0,1,2\\}^{\\mathbb{N}}$ we study the convergence and the selection at temperature zero of the Gibbs measure associated to a non\u2013locally constant H\u00f6lder potential which admits exactly two maximizing ergodic measures. These measures are Dirac measures at two different fixed points, and the potential is flatter at one of these two fixed points. We prove that there always is convergence but not necessarily to the Dirac measure at the point where the potential is the flattest. This is contrary to what was expected in light of the analogous problem in Aubry-Mather theory [N. Anantharaman et al., Discrete Contin. Dyn. Syst. Ser. B, 5 (2005), pp. 513\u2013528]. This is also contrary to the finite range case where the equilibrium state converges to the equi-barycenter of the two Dirac measures. Moreover, we emphasize the unexpected behavior of the Gibbs measure: the eigenmeasure selects one Dirac measure (at the point where the potential is the flattest), and the eigenfunction selects the other one (at the point where the potential is the sharpest).<\/jats:p>","DOI":"10.1137\/110826333","type":"journal-article","created":{"date-parts":[[2012,2,2]],"date-time":"2012-02-02T18:44:07Z","timestamp":1328208247000},"page":"243-260","source":"Crossref","is-referenced-by-count":18,"title":["Selection of Ground States in the Zero Temperature Limit for a One-Parameter Family of Potentials"],"prefix":"10.1137","volume":"11","author":[{"given":"A. T.","family":"Baraviera","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"R.","family":"Leplaideur","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"A. O.","family":"Lopes","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2012,2,2]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.3934\/dcdsb.2005.5.513"},{"key":"R2","doi-asserted-by":"crossref","unstructured":"A. T. Baraviera, A. O. Lopes, and J. K. Mengue,\n                      On the selection of subaction and measure for a subclass of potentials defined by P. Walters\n                      , Ergod. Theory Dynam. Systems, (2012), to appear.","DOI":"10.1017\/S014338571200034X"},{"key":"R3","doi-asserted-by":"crossref","unstructured":"R. Bowen,\n                      Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms\n                      , Lecture Notes in Math. 470, Springer-Verlag, New York, Berlin, 1975.","DOI":"10.1007\/BFb0081279"},{"key":"R4","first-page":"287","volume":"34","author":"Bousch T.","year":"2001","journal-title":"Ann. Sci. ENS"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/16\/2\/303"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1007\/s00220-010-0997-8"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1017\/S014338571000026X"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1017\/S0143385701001663"},{"key":"R9","unstructured":"J.P. Conze and Y. Guivarch,\n                      Croissance des sommes ergodiques\n                      , manuscript, circa 1993."},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1017\/S0143385707000491"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1007\/BF01048183"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1007\/s10955-006-9260-2"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1017\/S0143385701001250"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/18\/6\/023"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/5\/3\/001"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/9\/2\/002"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1007\/BF02571383"},{"key":"R18","first-page":"10","volume":"59","author":"Nekhoroshev N. N.","year":"2004","journal-title":"Vestnik Moskov. Univ. Ser. I Mat. Mekh., 1, (2004), pp. 11\u201317 (in Russian); translation in Moscow Univ. Math. Bull."},{"key":"R19","unstructured":"W. Parry and M. Pollicott,\n                      Zeta functions and the periodic orbit structure of hyperbolic dynamics\n                      , Ast\u00e9risque, 187\u2013188 (1990)."},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.2307\/2373810"},{"key":"R21","doi-asserted-by":"publisher","DOI":"10.1070\/RM1972v027n04ABEH001383"}],"container-title":["SIAM Journal on Applied Dynamical Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/110826333","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T12:21:36Z","timestamp":1787228496000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/110826333"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,1]]},"references-count":21,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2012,1]]}},"alternative-id":["10.1137\/110826333"],"URL":"https:\/\/doi.org\/10.1137\/110826333","relation":{},"ISSN":["1536-0040"],"issn-type":[{"value":"1536-0040","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,1]]}}}