{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T12:42:03Z","timestamp":1787316123043,"version":"build-2736575974"},"reference-count":32,"publisher":"World Scientific Pub Co Pte Ltd","issue":"12","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2014,12]]},"abstract":"<jats:p>\n                    The border collision normal form is a continuous piecewise affine map of \u211d\n                    <jats:sup>n<\/jats:sup>\n                    with applications in piecewise smooth bifurcation theory. We show that these maps have absolutely continuous invariant measures for an open set of parameter space and hence the attractors have Hausdorff (fractal) dimension n. If n = 2 the attractors have topological dimension two, i.e. they contain open sets, and if n &gt; 2 then they have topological dimension n generically.\n                  <\/jats:p>","DOI":"10.1142\/s0218127414501648","type":"journal-article","created":{"date-parts":[[2015,1,5]],"date-time":"2015-01-05T01:43:47Z","timestamp":1420422227000},"page":"1450164","source":"Crossref","is-referenced-by-count":5,"title":["Invariant Measures for the n-Dimensional Border Collision Normal Form"],"prefix":"10.1142","volume":"24","author":[{"given":"Paul","family":"Glendinning","sequence":"first","affiliation":[{"name":"School of Mathematics, University of Manchester, Manchester M13 9PL, UK"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"219","published-online":{"date-parts":[[2015,1,4]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.80.3049"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.59.4052"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1109\/81.847870"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1137\/0520080"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1016\/S0960-0779(98)00130-1"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1142\/S021812749900122X"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1017\/S0143385700000377"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1090\/pspum\/069\/1858553"},{"key":"rf9","first-page":"689","volume":"21","author":"Buzzi J.","year":"2001","journal-title":"Erg. 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