{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,8]],"date-time":"2025-09-08T06:42:57Z","timestamp":1757313777096},"reference-count":6,"publisher":"American Mathematical Society (AMS)","issue":"18","license":[{"start":{"date-parts":[[1998,10,29]],"date-time":"1998-10-29T00:00:00Z","timestamp":909619200000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. Res. Announc. Amer. Math. Soc."],"abstract":"<p>For a subshift of finite type and a fixed H\u00f6lder continuous function, the zero measure invariant set of points where the Birkhoff averages do not exist is either empty or carries <italic>full<\/italic> Hausdorff dimension. Similar statements hold for conformal repellers and two-dimensional horseshoes, and the set of points where the pointwise dimensions, local entropies, Lyapunov exponents, and Birkhoff averages do not exist simultaneously.<\/p>","DOI":"10.1090\/s1079-6762-97-00035-8","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T22:14:44Z","timestamp":1027721684000},"page":"114-118","source":"Crossref","is-referenced-by-count":7,"title":["Invariant sets with zero measure and full Hausdorff dimension"],"prefix":"10.1090","volume":"3","author":[{"given":"Luis","family":"Barreira","sequence":"first","affiliation":[]},{"given":"J\u00f6rg","family":"Schmeling","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[1997,10,29]]},"reference":[{"issue":"1","key":"1","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1090\/S1079-6762-96-00007-8","article-title":"On the pointwise dimension of hyperbolic measures: a proof of the Eckmann-Ruelle conjecture","volume":"2","author":"Barreira, Luis","year":"1996","journal-title":"Electron. Res. Announc. Amer. Math. Soc.","ISSN":"http:\/\/id.crossref.org\/issn\/1079-6762","issn-type":"print"},{"key":"2","unstructured":"L. Barreira, Ya. Pesin, and J. Schmeling, Dimension of hyperbolic measures\u2014a proof of the Eckmann\u2013Ruelle conjecture, WIAS Preprint 245 and IST Preprint 26\/96, 1996 (submitted for publication)."},{"key":"3","unstructured":"L. Barreira and J. Schmeling, Sets of \u201cnon-typical\u201d points have full topological entropy and full Hausdorff dimension, IST Preprint 14\/97, 1997 (submitted for publication)."},{"issue":"4","key":"4","first-page":"50","article-title":"Topological pressure and the variational principle for noncompact sets","volume":"18","author":"Pesin, Ya. B.","year":"1984","journal-title":"Funktsional. Anal. i Prilozhen.","ISSN":"http:\/\/id.crossref.org\/issn\/0374-1990","issn-type":"print"},{"key":"5","doi-asserted-by":"crossref","unstructured":"Ya. Pesin and H. Weiss, A multifractal analysis of Gibbs measures for conformal expanding maps and Markov Moran geometric constructions, J. Statist. Phys. 86 (1997), no. 1\/2, 233\u2013275.","DOI":"10.1007\/BF02180206"},{"key":"6","unstructured":"J. Schmeling and S. Troubetzkoy, Pointwise dimension for regular hyperbolic measures for endomorphisms, in preparation."}],"container-title":["Electronic Research Announcements of the American Mathematical Society"],"original-title":[],"language":"en","deposited":{"date-parts":[[2021,11,1]],"date-time":"2021-11-01T18:23:41Z","timestamp":1635791021000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/era\/1997-03-18\/S1079-6762-97-00035-8\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1997,10,29]]},"references-count":6,"journal-issue":{"issue":"18","published-online":{"date-parts":[[1997,10,29]]}},"alternative-id":["S1079-6762-97-00035-8"],"URL":"https:\/\/doi.org\/10.1090\/s1079-6762-97-00035-8","relation":{},"ISSN":["1079-6762"],"issn-type":[{"value":"1079-6762","type":"electronic"}],"subject":[],"published":{"date-parts":[[1997,10,29]]}}}