{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,15]],"date-time":"2024-09-15T22:27:01Z","timestamp":1726439221165},"reference-count":12,"publisher":"World Scientific Pub Co Pte Ltd","issue":"11","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2011,11]]},"abstract":"<jats:p> We study the bifurcation of limit cycles from the periodic orbits of a two-dimensional (resp. four-dimensional) linear center in \u211d<jats:sup>n<\/jats:sup> perturbed inside a class of discontinuous piecewise linear differential systems. Our main result shows that at most 1 (resp. 3) limit cycle can bifurcate up to first-order expansion of the displacement function with respect to the small parameter. This upper bound is reached. For proving these results, we use the averaging theory in a form where the differentiability of the system is not needed. <\/jats:p>","DOI":"10.1142\/s0218127411030441","type":"journal-article","created":{"date-parts":[[2012,1,2]],"date-time":"2012-01-02T20:28:03Z","timestamp":1325536083000},"page":"3181-3194","source":"Crossref","is-referenced-by-count":5,"title":["LIMIT CYCLES OF DISCONTINUOUS PIECEWISE LINEAR DIFFERENTIAL SYSTEMS"],"prefix":"10.1142","volume":"21","author":[{"given":"PEDRO TONIOL","family":"CARDIN","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1tica, IBILCE\u2013UNESP, CEP 15054-000, S. J. do Rio Preto, S\u00e3o Paulo, Brazil"}]},{"given":"TIAGO","family":"DE CARVALHO","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica, IBILCE\u2013UNESP, CEP 15054-000, S. J. do Rio Preto, S\u00e3o Paulo, Brazil"}]},{"given":"JAUME","family":"LLIBRE","sequence":"additional","affiliation":[{"name":"Departament de Matem\u00e0tiques, Universitat Aut\u00f2noma de Barcelona, 08193 Bellaterra, Barcelona, Spain"}]}],"member":"219","published-online":{"date-parts":[[2012,4,6]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1016\/B978-1-4831-6724-4.50014-9"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127405013599"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1137\/070701091"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1080\/14689360802534492"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-8159-4"},{"key":"rf6","series-title":"Applied Mathematical Sciences","volume-title":"Piecewise-Smooth Dynamical Systems","volume":"163","author":"di Bernardo M.","year":"2008"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1140-2"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1016\/S0362-546X(97)00669-X"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2009.10.002"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2009.08.022"},{"volume-title":"Degree Theory","year":"1978","author":"Lloyd N. G.","key":"rf11"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-61453-8"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127411030441","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T00:24:27Z","timestamp":1565137467000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127411030441"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,11]]},"references-count":12,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2012,4,6]]},"published-print":{"date-parts":[[2011,11]]}},"alternative-id":["10.1142\/S0218127411030441"],"URL":"https:\/\/doi.org\/10.1142\/s0218127411030441","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"type":"print","value":"0218-1274"},{"type":"electronic","value":"1793-6551"}],"subject":[],"published":{"date-parts":[[2011,11]]}}}