{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,8,10]],"date-time":"2023-08-10T14:16:12Z","timestamp":1691676972420},"reference-count":19,"publisher":"World Scientific Pub Co Pte Lt","issue":"11","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2005,11]]},"abstract":"<jats:p> The centralizer of a group element g is the group of elements commuting with g. Powers and, if existent, roots of g are contained in the centralizer. We call a centralizer trivial if it consists of the integer powers of g, only. <\/jats:p><jats:p> In the group of torus homeomorphisms, we study the centralizer of torus diffeomorphisms of hyperbolic Anosov type. As a result, the centralizer can be calculated, isomorphically, in the much smaller group of affine torus automorphisms. In particular, Anosov diffeomorphisms of the 2-torus with a unique fixed point possess trivial centralizer, up to a trivial involution. <\/jats:p><jats:p> The identification of individual reactors from data on reactor cascades, for example in chemical engineering, is one source of motivation for the study of roots of diffeomorphisms. Another possible source is the study of commuting diffeomorphisms in finite-dimensional spatially or spatio-temporally chaotic systems. <\/jats:p>","DOI":"10.1142\/s0218127405014325","type":"journal-article","created":{"date-parts":[[2006,2,6]],"date-time":"2006-02-06T04:49:18Z","timestamp":1139201358000},"page":"3691-3699","source":"Crossref","is-referenced-by-count":1,"title":["ROOTS AND CENTRALIZERS OF ANOSOV DIFFEOMORPHISMS ON TORI"],"prefix":"10.1142","volume":"15","author":[{"given":"BERNOLD","family":"FIEDLER","sequence":"first","affiliation":[{"name":"Brown University, Division of Applied Mathematics, 182 George Street, Providence, RI 02912, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1016\/0040-9383(76)90003-3"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0348-8079-4"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1975-0375287-X"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/1\/4\/001"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1017\/S0143385703000191"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1969-0253352-7"},{"key":"rf8","doi-asserted-by":"crossref","unstructured":"B.\u00a0Hasselblatt and A.\u00a0Katok (eds.), Handbook of Dynamical Systems\u00a01A (North-Holland, Amsterdam, 2002)\u00a0p. xii, 1220.","DOI":"10.1016\/S1874-575X(02)80003-0"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.3934\/dcds.1996.2.397"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1090\/pspum\/014\/0270396"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.2307\/2373551"},{"key":"rf12","author":"Mielke A.","journal-title":"Invent. 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