{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T14:37:14Z","timestamp":1772289434880,"version":"3.50.1"},"publisher-location":"Berlin, Heidelberg","reference-count":30,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783642388293","type":"print"},{"value":"9783642388309","type":"electronic"}],"license":[{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2013]]},"DOI":"10.1007\/978-3-642-38830-9_17","type":"book-chapter","created":{"date-parts":[[2013,9,20]],"date-time":"2013-09-20T10:08:51Z","timestamp":1379671731000},"page":"281-299","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Partial Symmetry Breaking and Heteroclinic Tangencies"],"prefix":"10.1007","author":[{"given":"Isabel S.","family":"Labouriau","sequence":"first","affiliation":[]},{"given":"Alexandre A. P.","family":"Rodrigues","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2013,7,12]]},"reference":[{"key":"17_CR1","first-page":"1","volume-title":"Nonlinear Dynamics and Turbulence","author":"V.S. Afraimovich","year":"1983","unstructured":"Afraimovich, V.S., Shilnikov, L.P.: Strange attractors and quasiattractors. In: Barenblatt, G.I., Iooss, G., Joseph, D.D. (eds.) Nonlinear Dynamics and Turbulence, pp.\u00a01\u201351. Pitman, Boston (1983)"},{"key":"17_CR2","doi-asserted-by":"publisher","first-page":"391","DOI":"10.1088\/0951-7715\/18\/1\/019","volume":"18","author":"M. Aguiar","year":"2005","unstructured":"Aguiar, M., Castro, S.B., Labouriau, I.S.: Dynamics near a heteroclinic network. Nonlinearity 18, 391\u2013414 (2005)","journal-title":"Nonlinearity"},{"issue":"2","key":"17_CR3","doi-asserted-by":"publisher","first-page":"369","DOI":"10.1142\/S021812740601485X","volume":"16","author":"M. Aguiar","year":"2006","unstructured":"Aguiar, M., Castro, S.B., Labouriau, I.S.: Simple vector fields with complex behaviour. Int. J. Bifurc. Chaos 16(2), 369\u2013381 (2006)","journal-title":"Int. J. Bifurc. Chaos"},{"issue":"1","key":"17_CR4","doi-asserted-by":"publisher","first-page":"75","DOI":"10.1080\/14689360903252119","volume":"25","author":"M. Aguiar","year":"2010","unstructured":"Aguiar, M., Labouriau, I.S., Rodrigues, A.A.P.: Swicthing near a heteroclinic network of rotating nodes. Dyn. Syst. Int. J. 25(1), 75\u201395 (2010)","journal-title":"Dyn. Syst. Int. J."},{"key":"17_CR5","volume-title":"Dynamics beyond uniform hyperbolicity","author":"C. Bonatti","year":"2005","unstructured":"Bonatti, C., D\u00edaz, L., Viana, M.: Dynamics beyond uniform hyperbolicity. Springer, Berlin\/Heidelberg (2005)"},{"key":"17_CR6","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1007\/BF01389849","volume":"29","author":"R. Bowen","year":"1975","unstructured":"Bowen, R.: A horseshoe with positive measure. Invent. Math. 29, 203\u2013204 (1975)","journal-title":"Invent. Math."},{"key":"17_CR7","doi-asserted-by":"crossref","DOI":"10.1007\/BFb0081279","volume-title":"Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms","author":"R. Bowen","year":"1975","unstructured":"Bowen, R.: Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms. Lecture Notes in Mathematics. Springer, Berlin\/New York (1975)"},{"key":"17_CR8","first-page":"87","volume":"200","author":"V.V. Bykov","year":"2000","unstructured":"Bykov, V.V.: Orbit structure in a neighbourhood of a separatrix cycle containing two Saddle-Foci. Am. Math. Soc. Transl. 200, 87\u201397 (2000)","journal-title":"Am. Math. Soc. Transl."},{"key":"17_CR9","doi-asserted-by":"publisher","first-page":"539","DOI":"10.1016\/S0294-1449(98)80001-2","volume":"15","author":"E. Colli","year":"1998","unstructured":"Colli, E.: Infinitely many coexisting strange attractors. Ann. Inst. Henri Poincar\u00e9 Anal. Non Lin\u00e9aire 15, 539\u2013579 (1998)","journal-title":"Ann. Inst. Henri Poincar\u00e9 Anal. Non Lin\u00e9aire"},{"key":"17_CR10","unstructured":"Field, M.: Lectures on Bifurcations, Dynamics and Symmetry. Pitman Research Notes in Mathematics Series, vol.\u00a0356. Longman, Harlow (1996)"},{"key":"17_CR11","volume-title":"The Symmetry Perspective","author":"M. Golubitsky","year":"2000","unstructured":"Golubitsky, M., Stewart, I.: The Symmetry Perspective, Birkhauser, Basel\/Boston (2000)"},{"issue":"2\u20134","key":"17_CR12","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1016\/S0898-1221(97)00124-7","volume":"34","author":"S.V. Gonchenko","year":"1997","unstructured":"Gonchenko, S.V., Shilnikov, L.P., Turaev, D.V.: Quasiattractors and homoclinic tangencies. Comput. Math. Appl. 34(2\u20134), 195\u2013227 (1997)","journal-title":"Comput. Math. Appl."},{"key":"17_CR13","doi-asserted-by":"publisher","first-page":"1115","DOI":"10.1016\/j.physd.2012.03.002","volume":"241","author":"S.V. Gonchenko","year":"2012","unstructured":"Gonchenko, S.V., Ovsyannikov, I.I., Turaev, D.V.: On the effect of invisibility of stable periodic orbits at homoclinic bifurcations. Phys. D 241, 1115\u20131122 (2012)","journal-title":"Phys. D"},{"key":"17_CR14","doi-asserted-by":"publisher","first-page":"411","DOI":"10.1088\/0951-7715\/15\/4\/304","volume":"15","author":"A.J. Homburg","year":"2002","unstructured":"Homburg, A.J.: Periodic attractors, strange attractors and hyperbolic dynamics near homoclinic orbit to a saddle-focus equilibria. Nonlinearity 15, 411\u2013428 (2002)","journal-title":"Nonlinearity"},{"key":"17_CR15","doi-asserted-by":"crossref","unstructured":"Homburg, A.J., Sandstede, B.: Homoclinic and Heteroclinic Bifurcations in Vector Fields. Handbook of Dynamical Systems, vol.\u00a03, pp.\u00a0379\u2013524. North Holland, Amsterdam (2010)","DOI":"10.1016\/S1874-575X(10)00316-4"},{"key":"17_CR16","doi-asserted-by":"publisher","first-page":"121","DOI":"10.1017\/S0143385700008270","volume":"15","author":"M. Krupa","year":"1995","unstructured":"Krupa, M., Melbourne, I.: Asymptotic stability of heteroclinic cycles in systems with symmetry. Ergod. Theory Dyn. Syst. 15, 121\u2013147 (1995)","journal-title":"Ergod. Theory Dyn. Syst."},{"issue":"8","key":"17_CR17","doi-asserted-by":"publisher","first-page":"2527","DOI":"10.1016\/j.jde.2012.06.009","volume":"253","author":"I.S. Labouriau","year":"2012","unstructured":"Labouriau, I.S., Rodrigues, A.A.P.: Global generic dynamics close to symmetry. J. Differ. Equ. 253(8), 2527\u20132557 (2012)","journal-title":"J. Differ. Equ."},{"key":"17_CR18","doi-asserted-by":"publisher","first-page":"78","DOI":"10.1016\/j.jde.2005.02.019","volume":"219","author":"J.S.W. Lamb","year":"2005","unstructured":"Lamb, J.S.W., Teixeira, M.A., Webster, K.N.: Heteroclinic bifurcations near Hopf-zero bifurcation in reversible vector fields in R\n                        3. J. Differ. Equ. 219, 78\u2013115 (2005)","journal-title":"J. Differ. Equ."},{"key":"17_CR19","doi-asserted-by":"publisher","first-page":"363","DOI":"10.1007\/978-94-010-0788-7_43","volume-title":"Dynamo and Dynamics, a Mathematical Challenge","author":"I. Melbourne","year":"2001","unstructured":"Melbourne, I., Proctor, M.R.E., Rucklidge, A.M.: A heteroclinic model of geodynamo reversals and excursions. In: Chossat, P., Armbruster, D., Oprea, I. (eds.) Dynamo and Dynamics, a Mathematical Challenge, pp.\u00a0363\u2013370. Kluwer, Dordrecht (2001)"},{"key":"17_CR20","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/BF02392766","volume":"171","author":"L. Mora","year":"1993","unstructured":"Mora, L., Viana, M.: Abundance of strange attractors. Acta Math. 171, 1\u201371 (1993)","journal-title":"Acta Math."},{"key":"17_CR21","doi-asserted-by":"publisher","first-page":"9","DOI":"10.1016\/0040-9383(74)90034-2","volume":"13","author":"S.E. Newhouse","year":"1974","unstructured":"Newhouse, S.E.: Diffeomorphisms with infinitely many sinks. Topology 13, 9\u201318 (1974)","journal-title":"Topology"},{"key":"17_CR22","doi-asserted-by":"publisher","first-page":"101","DOI":"10.1007\/BF02684771","volume":"50","author":"S.E. Newhouse","year":"1979","unstructured":"Newhouse, S.E.: The abundance of wild hyperbolic sets and non-smooth stable sets for diffeomorphisms. Publ. Math. Inst. Hautes Etudes Sci. 50, 101\u2013151 (1979)","journal-title":"Publ. Math. Inst. Hautes Etudes Sci."},{"key":"17_CR23","doi-asserted-by":"publisher","first-page":"557","DOI":"10.1070\/SM1987v058n02ABEH003120","volume":"58","author":"I.M. Ovsyannikov","year":"1987","unstructured":"Ovsyannikov, I.M., Shilnikov, L.P.: On systems with saddle-focus homoclinic curve. Math. USSR Sb. 58, 557\u2013574 (1987)","journal-title":"Math. USSR Sb."},{"key":"17_CR24","doi-asserted-by":"crossref","unstructured":"Rodrigues, A.A.P.: Repelling dynamics near a Bykov cycle. J. Dyn. Differ. Equ. (2013, to appear). doi:10.1007\/s10884-013-9289-2","DOI":"10.1007\/s10884-013-9289-2"},{"key":"17_CR25","unstructured":"Rodrigues, A.A.P., Labouriau, I.S.: Spiraling sets near a heteroclinic network. Preprint \u2013 CMUP n.\u00a02011\u201322 available at arXiv:1304.5283v1"},{"key":"17_CR26","first-page":"1255","volume":"13","author":"V.S. Samovol","year":"1972","unstructured":"Samovol, V.S.: Linearization of a system of differential equations in the neighbourhood of a singular point. Sov. Math. Dokl. 13, 1255\u20131959 (1972)","journal-title":"Sov. Math. Dokl."},{"issue":"103","key":"17_CR27","first-page":"443","volume":"61","author":"L.P. Shilnikov","year":"1963","unstructured":"Shilnikov, L.P.: Some cases of generation of periodic motion from singular trajectories. Math. USSR Sb. 61(103), 443\u2013466 (1963)","journal-title":"Math. USSR Sb."},{"key":"17_CR28","first-page":"163","volume":"6","author":"L.P. Shilnikov","year":"1965","unstructured":"Shilnikov, L.P.: A case of the existence of a denumerable set of periodic motions. Sov. Math. Dokl. 6, 163\u2013166 (1965)","journal-title":"Sov. Math. Dokl."},{"key":"17_CR29","doi-asserted-by":"publisher","first-page":"353","DOI":"10.1070\/SM1967v003n03ABEH002748","volume":"3","author":"L.P. Shilnikov","year":"1967","unstructured":"Shilnikov, L.P.: On a Poincar\u00e9\u2013Birkhoff problem. Math. USSR Sb. 3, 353\u2013371 (1967)","journal-title":"Math. USSR Sb."},{"issue":"1","key":"17_CR30","first-page":"54","volume":"8","author":"L.P. Shilnikov","year":"1967","unstructured":"Shilnikov, L.P.: The existence of a denumerable set of periodic motions in four dimensional space in an extended neighbourhood of a saddle-focus. Sov. Math. Dokl. 8(1), 54\u201358 (1967)","journal-title":"Sov. Math. Dokl."}],"container-title":["Springer Proceedings in Mathematics &amp; Statistics","Progress and Challenges in Dynamical Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-38830-9_17","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,2,14]],"date-time":"2023-02-14T01:29:51Z","timestamp":1676338191000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-642-38830-9_17"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"ISBN":["9783642388293","9783642388309"],"references-count":30,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-38830-9_17","relation":{},"ISSN":["2194-1009","2194-1017"],"issn-type":[{"value":"2194-1009","type":"print"},{"value":"2194-1017","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013]]},"assertion":[{"value":"12 July 2013","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}}]}}