{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,20]],"date-time":"2026-01-20T08:07:52Z","timestamp":1768896472438,"version":"3.49.0"},"reference-count":59,"publisher":"World Scientific Pub Co Pte Lt","issue":"08","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2014,8]]},"abstract":"<jats:p> We give a qualitative description of two main routes to chaos in three-dimensional maps. We discuss Shilnikov scenario of transition to spiral chaos and a scenario of transition to discrete Lorenz-like and figure-eight strange attractors. The theory is illustrated by numerical analysis of three-dimensional Henon-like maps and Poincar\u00e9 maps in models of nonholonomic mechanics. <\/jats:p>","DOI":"10.1142\/s0218127414400057","type":"journal-article","created":{"date-parts":[[2014,8,29]],"date-time":"2014-08-29T08:35:53Z","timestamp":1409301353000},"page":"1440005","source":"Crossref","is-referenced-by-count":45,"title":["Simple Scenarios of Onset of Chaos in Three-Dimensional Maps"],"prefix":"10.1142","volume":"24","author":[{"given":"Alexander","family":"Gonchenko","sequence":"first","affiliation":[{"name":"Research Institute of Applied Mathematics and Cybernetics, Lobachevsky State University of Nizhny Novgorod, ul. Ulyanova 10, Nizhny Novgorod 603005, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sergey","family":"Gonchenko","sequence":"additional","affiliation":[{"name":"Research Institute of Applied Mathematics and Cybernetics, Lobachevsky State University of Nizhny Novgorod, ul. Ulyanova 10, Nizhny Novgorod 603005, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alexey","family":"Kazakov","sequence":"additional","affiliation":[{"name":"Research Institute of Applied Mathematics and Cybernetics, Lobachevsky State University of Nizhny Novgorod, ul. Ulyanova 10, Nizhny Novgorod 603005, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dmitry","family":"Turaev","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2014,8,29]]},"reference":[{"key":"rf1","first-page":"206","volume":"15","author":"Afraimovich V. S.","year":"1974","journal-title":"Soviet Math. Dokl."},{"key":"rf2","first-page":"1761","volume":"15","author":"Afraimovich V. S.","year":"1974","journal-title":"Soviet Math. Dokl."},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8928(77)90112-5"},{"key":"rf4","first-page":"253","volume":"22","author":"Afraimovich V. S.","year":"1977","journal-title":"Soviet Phys. Dokl."},{"key":"rf5","first-page":"164","volume":"35","author":"Afraimovich V. S.","year":"1980","journal-title":"Russ. Math. Surv."},{"key":"rf6","first-page":"153","volume":"44","author":"Afraimovich V. S.","year":"1982","journal-title":"Trans. Mosc. Math. Soc."},{"key":"rf7","volume-title":"Nonlinear Dynamics and Turbulence","author":"Afraimovich V. S.","year":"1983"},{"key":"rf9","first-page":"720","volume":"33","author":"Afraimovich V. S.","year":"1988","journal-title":"Soviet Phys. Dokl."},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8928(89)90128-7"},{"key":"rf11","first-page":"88","volume":"31","author":"Anishenko V. S.","year":"2005","journal-title":"Letters to JTPH"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1007\/BF01209312"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1080\/03091928508219264"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1007\/BF01081886"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1007\/BF01213607"},{"key":"rf17","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127412300169"},{"key":"rf18","doi-asserted-by":"publisher","DOI":"10.1007\/BF01095124"},{"key":"rf19","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127405014222"},{"key":"rf20","doi-asserted-by":"publisher","DOI":"10.2307\/2944326"},{"key":"rf21","series-title":"Encyclopaedia of Mathematical Sciences","volume-title":"Dynamics Beyond Uniform Hyperbolicity: A Global Geometric and Probabilistic Perspective","volume":"102","author":"Bonatti C.","year":"2005"},{"key":"rf22","doi-asserted-by":"publisher","DOI":"10.1070\/PU2003v046n04ABEH001306"},{"key":"rf23","doi-asserted-by":"publisher","DOI":"10.1134\/S1560354712060044"},{"key":"rf24","first-page":"512","volume":"18","author":"Borisov A. V.","year":"2014","journal-title":"Reg. Chaot. Dyn."},{"key":"rf25","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(93)90283-7"},{"key":"rf26","first-page":"83","volume":"83","author":"Braaksma B. L. J.","year":"1990","journal-title":"Memoirs AMS"},{"key":"rf27","doi-asserted-by":"publisher","DOI":"10.1090\/memo\/0421"},{"key":"rf31","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(93)90288-C"},{"key":"rf33","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0101779"},{"key":"rf34","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/26\/1\/1"},{"key":"rf36","first-page":"410","volume":"47","author":"Gonchenko S. V.","year":"1993","journal-title":"Russ. Acad. Sci. Dokl. Math."},{"key":"rf37","doi-asserted-by":"publisher","DOI":"10.1063\/1.166154"},{"key":"rf38","first-page":"70","volume":"216","author":"Gonchenko S. V.","year":"1997","journal-title":"Proc. Steklov Inst. Math."},{"key":"rf39","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127405014180"},{"key":"rf40","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/21\/5\/003"},{"key":"rf41","first-page":"507","volume":"8","author":"Gonchenko A. S.","year":"2012","journal-title":"Rus. Nonlin. Dyn."},{"key":"rf42","first-page":"3","volume":"8","author":"Gonchenko A. S.","year":"2012","journal-title":"Rus. Nonlin. Dyn."},{"key":"rf43","doi-asserted-by":"publisher","DOI":"10.1016\/j.physd.2012.03.002"},{"key":"rf44","first-page":"77","volume":"9","author":"Gonchenko A. S.","year":"2013","journal-title":"Rus. Nonlin. Dyn."},{"key":"rf45","doi-asserted-by":"publisher","DOI":"10.1134\/S1560354713050055"},{"key":"rf46","first-page":"32","volume":"8","author":"Gonchenko S. V.","year":"2013","journal-title":"Math. Model. Nat. Phenom."},{"key":"rf47","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-6374-6_25"},{"key":"rf48","doi-asserted-by":"publisher","DOI":"10.1007\/BF02684769"},{"key":"rf49","doi-asserted-by":"publisher","DOI":"10.1134\/S1560354713050043"},{"key":"rf50","doi-asserted-by":"publisher","DOI":"10.1142\/S021812749300026X"},{"key":"rf51","volume-title":"Elements of Applied Bifurcation Theory","author":"Kuznetsov Yu. A.","year":"1998"},{"key":"rf52","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/2\/1\/009"},{"key":"rf53","doi-asserted-by":"publisher","DOI":"10.1007\/BF02392766"},{"key":"rf54","doi-asserted-by":"publisher","DOI":"10.1016\/0040-9383(74)90034-2"},{"key":"rf55","doi-asserted-by":"publisher","DOI":"10.1070\/SM1987v058n02ABEH003120"},{"key":"rf57","first-page":"163","volume":"6","author":"Shilnikov L. P.","year":"1965","journal-title":"Soviet Math. Dokl."},{"key":"rf58","doi-asserted-by":"publisher","DOI":"10.1070\/SM1967v003n01ABEH002362"},{"key":"rf59","doi-asserted-by":"publisher","DOI":"10.1070\/SM1970v010n01ABEH001588"},{"key":"rf63","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127491000567"},{"key":"rf64","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(93)90292-9"},{"key":"rf65","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127493000933"},{"key":"rf67","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127496000515"},{"key":"rf68","doi-asserted-by":"publisher","DOI":"10.1070\/SM1998v189n02ABEH000300"},{"key":"rf69","first-page":"23","volume":"467","author":"Turaev D. V.","year":"2008","journal-title":"Russ. Dokl. Math."},{"key":"rf70","doi-asserted-by":"publisher","DOI":"10.1017\/S0143385700009895"},{"key":"rf72","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0068363"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127414400057","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T20:32:10Z","timestamp":1565123530000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127414400057"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,8]]},"references-count":59,"journal-issue":{"issue":"08","published-online":{"date-parts":[[2014,8,29]]},"published-print":{"date-parts":[[2014,8]]}},"alternative-id":["10.1142\/S0218127414400057"],"URL":"https:\/\/doi.org\/10.1142\/s0218127414400057","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,8]]}}}