{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T22:09:46Z","timestamp":1648591786222},"reference-count":11,"publisher":"World Scientific Pub Co Pte Lt","issue":"08","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2012,8]]},"abstract":"<jats:p> In this article, we study statistical attractors of skew products which have an m-dimensional compact manifold M as a fiber and their \u03b5-invisible subsets. For any n \u2265 100 m<jats:sup>2<\/jats:sup>, m = dim (M), we construct a set [Formula: see text] in the space of skew products over the horseshoe with the fiber M having the following properties. Each C<jats:sup>2<\/jats:sup>-skew product from [Formula: see text] possesses a statistical attractor with an \u03b5-invisible part, for an extraordinary value of \u03b5 (\u03b5 = (m + 1)<jats:sup>-n<\/jats:sup>), whose size of invisibility is comparable to that of the whole attractor, and the Lipschitz constants of the map and its inverse are no longer than L. The set [Formula: see text] is a ball of radius O(n<jats:sup>-3<\/jats:sup>) in the space of skew products over the horseshoe with the C<jats:sup>1<\/jats:sup>-metric. In particular, small perturbations of these skew products in the space of all diffeomorphisms still have attractors with the same properties. Moreover, for skew products which have an m-sphere as a fiber, it consists of structurally stable skew products. Our construction develops the example of [Ilyashenko &amp; Negut, 2010] to skew products which have an m-dimensional compact manifold as a fiber, m \u2265 2. <\/jats:p>","DOI":"10.1142\/s0218127412501829","type":"journal-article","created":{"date-parts":[[2012,9,17]],"date-time":"2012-09-17T04:52:34Z","timestamp":1347857554000},"page":"1250182","source":"Crossref","is-referenced-by-count":1,"title":["ATTRACTORS AND THEIR INVISIBLE PARTS FOR SKEW PRODUCTS WITH HIGH DIMENSIONAL FIBER"],"prefix":"10.1142","volume":"22","author":[{"given":"F. H.","family":"GHANE","sequence":"first","affiliation":[{"name":"Department of Mathematics, Ferdowsi University of Mashhad, Mashhad, P. O. Box 1159-91775, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M.","family":"NAZARI","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Ferdowsi University of Mashhad, Mashhad, P. O. Box 1159-91775, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M.","family":"SALEH","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Ferdowsi University of Mashhad, Mashhad, P. O. Box 1159-91775, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Z.","family":"SHABANI","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Ferdowsi University of Mashhad, Mashhad, P. O. Box 1159-91775, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2012,9,17]]},"reference":[{"key":"rf1","series-title":"Lecture Notes in Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/BFb0081279","volume-title":"Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms","volume":"410","author":"Bowen R.","year":"1975"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1142\/S0219493710002899"},{"key":"rf3","first-page":"84","volume":"1","author":"Gorodetsky A.","journal-title":"Vestnic MSU"},{"key":"rf4","first-page":"95","volume":"33","author":"Gorodetsky A.","journal-title":"Funksional. Anals. Prizlohen"},{"key":"rf5","first-page":"96","volume":"231","author":"Gorodetsky A.","journal-title":"Proc. Steklov Inst. 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