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The occurrence of such degenerate bifurcations is particularly important in piecewise smooth maps, for which it is not possible to specify in general the result of the bifurcation, as it strongly depends on the global properties of the map. In fact, the degenerate bifurcations mainly occur in piecewise smooth maps defined in some subspace of the phase space by a linear or linear-fractional function, although not necessarily only by such functions. We also discuss the relation between degenerate bifurcations and border-collision bifurcations. <\/jats:p>","DOI":"10.1142\/s0218127410026927","type":"journal-article","created":{"date-parts":[[2010,7,19]],"date-time":"2010-07-19T06:47:03Z","timestamp":1279522023000},"page":"2045-2070","source":"Crossref","is-referenced-by-count":110,"title":["DEGENERATE BIFURCATIONS AND BORDER COLLISIONS IN PIECEWISE SMOOTH 1D AND 2D MAPS"],"prefix":"10.1142","volume":"20","author":[{"given":"IRYNA","family":"SUSHKO","sequence":"first","affiliation":[{"name":"Institute of Mathematics, National Academy of Sciences of Ukraine, Kyiv School of Economics, Kyiv, Ukraine"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"LAURA","family":"GARDINI","sequence":"additional","affiliation":[{"name":"Department of Economics and Quantitative Methods, University of Urbino, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"219","published-online":{"date-parts":[[2012,5,2]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/19\/3\/001"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.59.4052"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1109\/81.841921"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1109\/81.847870"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-78043-1"},{"key":"rf8","first-page":"1881","volume":"10","author":"di Bernardo M.","journal-title":"Chaos Solit. 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