{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,10]],"date-time":"2026-04-10T11:13:23Z","timestamp":1775819603938,"version":"3.50.1"},"reference-count":13,"publisher":"American Mathematical Society (AMS)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Proc. Amer. Math. Soc."],"abstract":"<p>We show that, among area contracting embeddings of the 2-disk, infinitely renormalizable maps with a bounded geometry either have positive topological entropy or correspond to a cascade of period doubling.<\/p>","DOI":"10.1090\/s0002-9939-98-03945-8","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T18:13:45Z","timestamp":1027707225000},"page":"297-304","source":"Crossref","is-referenced-by-count":3,"special_numbering":"463","title":["Infinitely renormalizable diffeomorphisms of the disk at the boundary of chaos"],"prefix":"10.1090","volume":"126","author":[{"given":"Eleonora","family":"Catsigeras","sequence":"first","affiliation":[]},{"given":"Jean-Marc","family":"Gambaudo","sequence":"additional","affiliation":[]},{"given":"Fernando","family":"Moreira","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[1998,1]]},"reference":[{"issue":"4","key":"1","doi-asserted-by":"publisher","first-page":"337","DOI":"10.1016\/0040-9383(76)90026-4","article-title":"The periodic points of maps of the disk and the interval","volume":"15","author":"Bowen, Rufus","year":"1976","journal-title":"Topology","ISSN":"https:\/\/id.crossref.org\/issn\/0040-9383","issn-type":"print"},{"key":"2","unstructured":"[Ca] E. Catsigeras, \u201cCascades of period doubling of stable codimension one,\u201d IMPA\u2019s thesis, 1994."},{"key":"3","doi-asserted-by":"crossref","unstructured":"[CT] P. Coullet and C. Tresser, \u201cIt\u00e9rations d\u2019endomorphismes et groupe de renormalisation,\u201d J. Phys. C5 (1978),25\u201328.","DOI":"10.1051\/jphyscol:1978513"},{"issue":"2","key":"4","doi-asserted-by":"publisher","first-page":"287","DOI":"10.1088\/0951-7715\/2\/2\/005","article-title":"H\u00e9non-like maps with strange attractors: there exist \ud835\udc36^{\u221e} Kupka-Smale diffeomorphisms on \ud835\udc46\u00b2 with neither sinks nor sources","volume":"2","author":"Gambaudo, J.-M.","year":"1989","journal-title":"Nonlinearity","ISSN":"https:\/\/id.crossref.org\/issn\/0951-7715","issn-type":"print"},{"key":"5","isbn-type":"print","doi-asserted-by":"publisher","first-page":"13","DOI":"10.1007\/978-94-011-3442-2_2","article-title":"How horseshoes are created","author":"Gambaudo, Jean-Marc","year":"1991","ISBN":"https:\/\/id.crossref.org\/isbn\/0792311531"},{"issue":"1","key":"6","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1007\/BF02096564","article-title":"Self-similar constructions in smooth dynamics: rigidity, smoothness and dimension","volume":"150","author":"Gambaudo, Jean-Marc","year":"1992","journal-title":"Comm. Math. Phys.","ISSN":"https:\/\/id.crossref.org\/issn\/0010-3616","issn-type":"print"},{"issue":"1","key":"7","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1007\/BF01020332","article-title":"Quantitative universality for a class of nonlinear transformations","volume":"19","author":"Feigenbaum, Mitchell J.","year":"1978","journal-title":"J. Statist. Phys.","ISSN":"https:\/\/id.crossref.org\/issn\/0022-4715","issn-type":"print"},{"key":"8","unstructured":"[Hu] J. Hu, \u201cRenormalization, rigidity and universality in bifurcation theory\u201d, Ph. D. Dissertation, CUNY (1995)."},{"key":"9","unstructured":"[HT] J. Hu and C. Tresser, \u201cPeriod Doubling, Entropy, and Renormalization\u201d preprint (1995)."},{"key":"10","series-title":"Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)]","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-78043-1","volume-title":"One-dimensional dynamics","volume":"25","author":"de Melo, Welington","year":"1993","ISBN":"https:\/\/id.crossref.org\/isbn\/3540564128"},{"issue":"2","key":"11","first-page":"167","article-title":"Horseshoes for mappings of the interval","volume":"27","author":"Misiurewicz, Micha\u0142","year":"1979","journal-title":"Bull. Acad. Polon. Sci. S\\'{e}r. Sci. Math."},{"key":"12","isbn-type":"print","first-page":"417","article-title":"Bounds, quadratic differentials, and renormalization conjectures","author":"Sullivan, Dennis","year":"1992","ISBN":"https:\/\/id.crossref.org\/isbn\/0821801678"},{"issue":"7","key":"13","first-page":"A577--A580","article-title":"It\u00e9rations d\u2019endomorphismes et groupe de renormalisation","volume":"287","author":"Tresser, Charles","year":"1978","journal-title":"C. R. Acad. Sci. Paris S\\'{e}r. A-B","ISSN":"https:\/\/id.crossref.org\/issn\/0151-0509","issn-type":"print"}],"container-title":["Proceedings of the American Mathematical Society"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/proc\/1998-126-01\/S0002-9939-98-03945-8\/S0002-9939-98-03945-8.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/proc\/1998-126-01\/S0002-9939-98-03945-8\/S0002-9939-98-03945-8.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,10]],"date-time":"2026-04-10T10:19:02Z","timestamp":1775816342000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/proc\/1998-126-01\/S0002-9939-98-03945-8\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,1]]},"references-count":13,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1998,1]]}},"alternative-id":["S0002-9939-98-03945-8"],"URL":"https:\/\/doi.org\/10.1090\/s0002-9939-98-03945-8","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6826","0002-9939"],"issn-type":[{"value":"1088-6826","type":"electronic"},{"value":"0002-9939","type":"print"}],"subject":[],"published":{"date-parts":[[1998,1]]}}}