{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,21]],"date-time":"2025-09-21T17:32:32Z","timestamp":1758475952211},"reference-count":15,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2016,11,16]],"date-time":"2016-11-16T00:00:00Z","timestamp":1479254400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Nonlinear Sci"],"published-print":{"date-parts":[[2017,4]]},"DOI":"10.1007\/s00332-016-9347-0","type":"journal-article","created":{"date-parts":[[2016,11,17]],"date-time":"2016-11-17T00:59:41Z","timestamp":1479344381000},"page":"661-685","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Topological Equivalences for One-parameter Bifurcations of Scalar Maps"],"prefix":"10.1007","volume":"27","author":[{"given":"Francisco","family":"Balibrea","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Henrique M.","family":"Oliveira","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jose C.","family":"Valverde","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2016,11,16]]},"reference":[{"key":"9347_CR1","series-title":"A Series of Comprehensive Studies in Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4684-0147-9","volume-title":"Geometrical Methods in the Theory of Ordinary Differential Equations, Grundleheren der mathematischen Wissenschaften","author":"VI Arnold","year":"1983","unstructured":"Arnold, V.I.: Geometrical Methods in the Theory of Ordinary Differential Equations, Grundleheren der mathematischen Wissenschaften. A Series of Comprehensive Studies in Mathematics, vol. 250. Springer, Berlin (1983)"},{"key":"9347_CR2","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-57884-7","volume-title":"Dynamical Systems V. Encyclopaedia of Mathematical Sciences","author":"V Arnol\u2019d","year":"1994","unstructured":"Arnol\u2019d, V., Afraimovich, V., Il\u2019yashenko, Y., Shil\u2019nikov, L.: Bifurcation theory. In: Arnold, V. (ed.) Dynamical Systems V. Encyclopaedia of Mathematical Sciences. Springer, New York (1994)"},{"key":"9347_CR3","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1006\/jmaa.1999.6460","volume":"237","author":"F Balibrea","year":"1999","unstructured":"Balibrea, F., Valverde, J.C.: Bifurcations under non-degenerated conditions of higher degree and a new simple proof of the Hopf-Neimark-Sacker bifurcation theorem. J. Math. Anal. Appl. 237, 93\u2013105 (1999)","journal-title":"J. Math. Anal. Appl."},{"key":"9347_CR4","doi-asserted-by":"crossref","first-page":"155","DOI":"10.4995\/agt.2001.2146","volume":"2","author":"F Balibrea","year":"2000","unstructured":"Balibrea, F., Valverde, J.C.: Topological normal forms of higher degree for the simplest bifurcations. Appl. Gen. Topol. 2, 155\u2013164 (2000)","journal-title":"Appl. Gen. Topol."},{"key":"9347_CR5","doi-asserted-by":"crossref","unstructured":"Carr, J.: Applications of Center Manifold Theory. In: Applied Mathematical Sciences, vol. 35. Springer, New York (1981)","DOI":"10.1007\/978-1-4612-5929-9"},{"key":"9347_CR6","volume-title":"One Dimensional Dynamics (Ergebnisse der Mathematik und ihrer Grenzgebiete)","author":"W Melo de","year":"1993","unstructured":"de Melo, W., Van Strien, S.: One Dimensional Dynamics (Ergebnisse der Mathematik und ihrer Grenzgebiete), vol. 25. Springer, Berlin (1993)"},{"key":"9347_CR7","unstructured":"Diekmann, O. Kuznetsov, Y.A.: Lecture Notes on Dynamical Systems. Retrieved on 20 June 2016 http:\/\/www.staff.science.uu.nl\/kouzn101\/NLDV\/Lect10_11 (2016)"},{"key":"9347_CR8","volume-title":"An Introduction to Difference Equations. Undergraduate Texts in Mathematics","author":"SN Elaydi","year":"2005","unstructured":"Elaydi, S.N.: An Introduction to Difference Equations. Undergraduate Texts in Mathematics, 3rd edn. Springer, Berlin (2005). ISBN 0-387-23059-9","edition":"3"},{"issue":"2","key":"9347_CR9","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1007\/BF01390107","volume":"39","author":"J Guckenheimer","year":"1977","unstructured":"Guckenheimer, J.: On the bifurcation of maps of the interval. Invent. Math. 39(2), 165\u2013178 (1977)","journal-title":"Invent. Math."},{"key":"9347_CR10","doi-asserted-by":"crossref","unstructured":"Guckenheimer, J., Holmes, P.: Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields. In: Applied Mathematical Sciences, vol. 42. Springer, New York (1983)","DOI":"10.1007\/978-1-4612-1140-2"},{"key":"9347_CR11","unstructured":"Kuznetsov, Y.A.: Elements of Applied Bifurcation Theory. In: Applied Mathematical Sciences, 2nd edn., vol. 112. Springer, New York (1998)"},{"key":"9347_CR12","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1007\/BF02698773","volume":"57","author":"S Newhouse","year":"1983","unstructured":"Newhouse, S., Palis, J., Takens, F.: Bifurcations and stability of families of diffeomorphisms. Publ. Math. L\u2019I.H.E.S. 57, 5\u201371 (1983)","journal-title":"Publ. Math. L\u2019I.H.E.S."},{"issue":"6","key":"9347_CR13","doi-asserted-by":"crossref","first-page":"1552","DOI":"10.1137\/0522099","volume":"22","author":"BB Peckhamt","year":"1991","unstructured":"Peckhamt, B.B., Kevrekidis, I.G.: Period doubling with higher-order degeneracies. SIAM J. Math. Anal. 22(6), 1552\u20131574 (1991)","journal-title":"SIAM J. Math. Anal."},{"key":"9347_CR14","volume-title":"Sur les Propi\u00e9t\u00e9s des Fonctions D\u00e9finies par les \u00c9quations aux Diff\u00e9rences Partielles, Oeuvres","author":"H Poincar\u00e9","year":"1929","unstructured":"Poincar\u00e9, H.: Sur les Propi\u00e9t\u00e9s des Fonctions D\u00e9finies par les \u00c9quations aux Diff\u00e9rences Partielles, Oeuvres. Gauthier-Villars, Paris (1929)"},{"key":"9347_CR15","doi-asserted-by":"crossref","unstructured":"Wiggins, S.: Introduction to Applied Nonlinear Systems and Chaos. In: Texts in Applied Mathematics, vol. 2. Springer, New York (1990)","DOI":"10.1007\/978-1-4757-4067-7"}],"container-title":["Journal of Nonlinear Science"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00332-016-9347-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00332-016-9347-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00332-016-9347-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,15]],"date-time":"2019-09-15T13:42:01Z","timestamp":1568554921000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00332-016-9347-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,11,16]]},"references-count":15,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2017,4]]}},"alternative-id":["9347"],"URL":"https:\/\/doi.org\/10.1007\/s00332-016-9347-0","relation":{},"ISSN":["0938-8974","1432-1467"],"issn-type":[{"value":"0938-8974","type":"print"},{"value":"1432-1467","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,11,16]]}}}