{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,27]],"date-time":"2026-02-27T23:49:22Z","timestamp":1772236162686,"version":"3.50.1"},"reference-count":12,"publisher":"World Scientific Pub Co Pte Ltd","issue":"07","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China (CN)","doi-asserted-by":"publisher","award":["11231001"],"award-info":[{"award-number":["11231001"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2016,6,30]]},"abstract":"<jats:p> Let [Formula: see text] be a compact metric space and [Formula: see text] a countable infinite discrete amenable group acting on [Formula: see text]. Like in the [Formula: see text]-action cases we define the notion of local entropy and by it we bound the difference between metric entropy and that of a partition, and bound the difference between topological entropy and that of a separated set, which generalize Theorems 1(1) and 1(2) in [Newhouse, 1989] from [Formula: see text]-actions to amenable group actions. We further prove that the entropy function [Formula: see text] is upper semi-continuous on [Formula: see text] for an asymptotic entropy expansive amenable group action. <\/jats:p>","DOI":"10.1142\/s0218127416501108","type":"journal-article","created":{"date-parts":[[2016,7,15]],"date-time":"2016-07-15T06:00:50Z","timestamp":1468562450000},"page":"1650110","source":"Crossref","is-referenced-by-count":2,"title":["Local Entropy, Metric Entropy and Topological Entropy for Countable Discrete Amenable Group Actions"],"prefix":"10.1142","volume":"26","author":[{"given":"Xiankun","family":"Ren","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Peking University, Beijing 100871, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wenxiang","family":"Sun","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Peking University, Beijing 100871, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2016,7,15]]},"reference":[{"key":"S0218127416501108BIB001","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1972-0285689-X"},{"key":"S0218127416501108BIB002","doi-asserted-by":"publisher","DOI":"10.1007\/BF02773637"},{"key":"S0218127416501108BIB003","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfa.2014.12.013"},{"key":"S0218127416501108BIB004","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfa.2011.04.014"},{"key":"S0218127416501108BIB005","doi-asserted-by":"publisher","DOI":"10.1007\/s002220100162"},{"key":"S0218127416501108BIB006","first-page":"903","volume":"21","author":"Misiurewicz M.","year":"1973","journal-title":"Bull. Acad. Polon. Sci. Sr. Sci. Math. Astronom. Phys."},{"key":"S0218127416501108BIB007","doi-asserted-by":"crossref","first-page":"175","DOI":"10.4064\/sm-55-2-175-200","volume":"55","author":"Misiurewicz M.","year":"1976","journal-title":"Studia Math."},{"key":"S0218127416501108BIB008","doi-asserted-by":"publisher","DOI":"10.2307\/1971492"},{"key":"S0218127416501108BIB009","doi-asserted-by":"crossref","first-page":"151","DOI":"10.4064\/sm-72-2-151-159","volume":"72","author":"Ollagnier J. M.","year":"1982","journal-title":"Studia Math."},{"key":"S0218127416501108BIB010","series-title":"Lecture Notes Math.","doi-asserted-by":"crossref","DOI":"10.1007\/BFb0101575","volume-title":"Ergodic Theory and Statistical Mechanic","volume":"1115","author":"Ollagnier J. M.","year":"1985"},{"key":"S0218127416501108BIB011","doi-asserted-by":"publisher","DOI":"10.1007\/BF02790325"},{"key":"S0218127416501108BIB012","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-5775-2"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127416501108","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,24]],"date-time":"2019-09-24T01:38:22Z","timestamp":1569289102000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127416501108"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,6,30]]},"references-count":12,"journal-issue":{"issue":"07","published-online":{"date-parts":[[2016,7,15]]},"published-print":{"date-parts":[[2016,6,30]]}},"alternative-id":["10.1142\/S0218127416501108"],"URL":"https:\/\/doi.org\/10.1142\/s0218127416501108","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,6,30]]}}}