{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T06:42:43Z","timestamp":1740120163635,"version":"3.37.3"},"reference-count":17,"publisher":"World Scientific Pub Co Pte Ltd","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2019,6,15]]},"abstract":"<jats:p> A dynamical system possessing an equilibrium point with two zero eigenvalues is considered. We assume that a degenerate Bogdanov\u2013Takens bifurcation with symmetry of order two is present and, in the parameter space, a curve of heteroclinic bifurcation values emerges from the codimension two bifurcation point. Using a blow-up transformation and a perturbation method, we obtain second order approximations both for the heteroclinic orbits and for the curve of heteroclinic bifurcation values. Applications of our results for the truncated normal form and for a Li\u00e9nard equation are presented. Some numerical simulations illustrating the accuracy of our results are performed. <\/jats:p>","DOI":"10.1142\/s0218127419500743","type":"journal-article","created":{"date-parts":[[2019,7,1]],"date-time":"2019-07-01T03:08:51Z","timestamp":1561950531000},"page":"1950074","source":"Crossref","is-referenced-by-count":0,"title":["Approximations of the Heteroclinic Orbits Near a Double-Zero Bifurcation with Symmetry of Order Two. Application to a Li\u00e9nard Equation"],"prefix":"10.1142","volume":"29","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3000-4235","authenticated-orcid":false,"given":"Carmen","family":"Roc\u015foreanu","sequence":"first","affiliation":[{"name":"Department of Statistics and Computer Science, University of Craiova, 13 A.I. Cuza, Craiova, Romania"}]},{"given":"Mihaela","family":"Sterpu","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Craiova, 13 A.I. Cuza, Craiova, Romania"}]}],"member":"219","published-online":{"date-parts":[[2019,7]]},"reference":[{"key":"S0218127419500743BIB001","doi-asserted-by":"publisher","DOI":"10.1137\/15M1017491"},{"key":"S0218127419500743BIB002","doi-asserted-by":"publisher","DOI":"10.1016\/S0960-0779(99)00144-7"},{"key":"S0218127419500743BIB003","doi-asserted-by":"publisher","DOI":"10.1023\/A:1008316010341"},{"key":"S0218127419500743BIB004","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-009-9489-9"},{"key":"S0218127419500743BIB005","doi-asserted-by":"publisher","DOI":"10.1016\/j.jsv.2008.11.015"},{"key":"S0218127419500743BIB006","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511665639.005"},{"key":"S0218127419500743BIB007","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-014-1604-x"},{"key":"S0218127419500743BIB008","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898718195"},{"key":"S0218127419500743BIB009","doi-asserted-by":"publisher","DOI":"10.1142\/S021812741250294X"},{"key":"S0218127419500743BIB010","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/11\/6\/005"},{"key":"S0218127419500743BIB011","first-page":"163","volume":"5","author":"Khorosov E. I.","year":"1979","journal-title":"Trans. Petrovski Sem."},{"key":"S0218127419500743BIB012","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-3978-7"},{"key":"S0218127419500743BIB013","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127414500576"},{"key":"S0218127419500743BIB014","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127415501254"},{"key":"S0218127419500743BIB015","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127416501431"},{"key":"S0218127419500743BIB016","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127417501097"},{"key":"S0218127419500743BIB017","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2008.10.024"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127419500743","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T14:39:28Z","timestamp":1565102368000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127419500743"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,6,15]]},"references-count":17,"journal-issue":{"issue":"06","published-online":{"date-parts":[[2019,7]]},"published-print":{"date-parts":[[2019,6,15]]}},"alternative-id":["10.1142\/S0218127419500743"],"URL":"https:\/\/doi.org\/10.1142\/s0218127419500743","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"type":"print","value":"0218-1274"},{"type":"electronic","value":"1793-6551"}],"subject":[],"published":{"date-parts":[[2019,6,15]]}}}