{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,29]],"date-time":"2025-10-29T18:35:44Z","timestamp":1761762944270},"reference-count":18,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2011,11,14]],"date-time":"2011-11-14T00:00:00Z","timestamp":1321228800000},"content-version":"unspecified","delay-in-days":6161,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Proceedings of the Royal Society of Edinburgh: Section A Mathematics"],"published-print":{"date-parts":[[1995]]},"abstract":"<jats:p>This paper addresses the realisation of ordinary differential equations (ODEs) by retarded functional differential equations (FDEs) in finite-dimensional invariant manifolds, locally around equilibrium points. A necessary and sufficient condition for realisability of <jats:italic>C<\/jats:italic><jats:sup>1<\/jats:sup> vector fields is established in terms of their linearisations at the equilibrium.<\/jats:p><jats:p>It is also shown that any arbitrary finite jet of vector fields of ODEs can be realised without any further restrictions than those imposed by the realisability of its linear term, a fact of relevance for discussing the flows defined by FDEs around singularities, and their bifurcations. Besides, it is proved that such a realisation can always be achieved with FDEs whose nonlinearities are defined in terms of a finite number of delayed values of the solutions.<\/jats:p>","DOI":"10.1017\/s030821050003033x","type":"journal-article","created":{"date-parts":[[2011,11,14]],"date-time":"2011-11-14T13:21:24Z","timestamp":1321276884000},"page":"759-776","source":"Crossref","is-referenced-by-count":13,"title":["Realisation of ordinary differential equations by retarded functional differential equations in neighbourhoods of equilibrium points"],"prefix":"10.1017","volume":"125","author":[{"given":"Teresa","family":"Faria","sequence":"first","affiliation":[]},{"given":"Luis T.","family":"Magalh\u00e3es","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2011,11,14]]},"reference":[{"key":"S030821050003033X_ref017","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-87284-6"},{"key":"S030821050003033X_ref018","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-6392-0"},{"key":"S030821050003033X_ref001","volume-title":"Chapitres Suppl\u00e9mentaires de la Th\u00e9orie des Equations Diff\u00e9rentielles Ordinaires","author":"Arnold","year":"1980"},{"key":"S030821050003033X_ref015","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1992-1089411-7"},{"key":"S030821050003033X_ref009","doi-asserted-by":"publisher","DOI":"10.1017\/S030821050002076X"},{"key":"S030821050003033X_ref010","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/056\/855090"},{"key":"S030821050003033X_ref016","first-page":"21","article-title":"\u00dcber die normal form anlytischer Differential\u2014Gleichungen in der N\u00e4he einer Gleichgewichtl\u00f6sung","author":"Siegel","year":"1952","journal-title":"Nach. 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IV"}],"container-title":["Proceedings of the Royal Society of Edinburgh: Section A Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S030821050003033X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,14]],"date-time":"2019-05-14T20:29:12Z","timestamp":1557865752000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S030821050003033X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995]]},"references-count":18,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1995]]}},"alternative-id":["S030821050003033X"],"URL":"https:\/\/doi.org\/10.1017\/s030821050003033x","relation":{},"ISSN":["0308-2105","1473-7124"],"issn-type":[{"value":"0308-2105","type":"print"},{"value":"1473-7124","type":"electronic"}],"subject":[],"published":{"date-parts":[[1995]]}}}