{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,2]],"date-time":"2022-04-02T14:23:23Z","timestamp":1648909403748},"reference-count":12,"publisher":"World Scientific Pub Co Pte Lt","issue":"07","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2003,7]]},"abstract":"<jats:p> Let a(x), b(x), p(x) be formal power series in the indeterminate x over [Formula: see text] (i.e. elements of the ring [Formula: see text] of such series) such that ord a(x) = 0, ord p(x) = 1 and p(x) is embeddable into an analytic iteration group [Formula: see text] in [Formula: see text]. By a covariant embedding of the linear functional equation [Formula: see text] (for the unknown series [Formula: see text]) with respect to [Formula: see text]. In this paper we solve the system ((Co1), (Co2)) (of so-called cocycle equations) completely, describe when and how the boundary conditions (B1) and (B2) can be satisfied, and present a large class of equations (L) together with iteration groups [Formula: see text] for which there exist covariant embeddings of (L) with respect to [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s0218127403007680","type":"journal-article","created":{"date-parts":[[2003,8,28]],"date-time":"2003-08-28T09:49:31Z","timestamp":1062064171000},"page":"1853-1875","source":"Crossref","is-referenced-by-count":2,"title":["On Covariant Embeddings of a Linear Functional Equation with Respect to an Analytic Iteration Group"],"prefix":"10.1142","volume":"13","author":[{"given":"Harald","family":"Fripertinger","sequence":"first","affiliation":[{"name":"Institut f\u00fcr Mathematik, Karl-Franzens-Universit\u00e4t Graz, Heinrichstr. 36\/4, A-8010 Graz, Austria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ludwig","family":"Reich","sequence":"additional","affiliation":[{"name":"Institut f\u00fcr Mathematik, Karl-Franzens-Universit\u00e4t Graz, Heinrichstr. 36\/4, A-8010 Graz, Austria"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","volume-title":"Elementary Theory of Analytic Functions of One or Several Complex Variables","author":"Cartan H.","year":"1963"},{"key":"rf2","volume-title":"Elementare Theorie der analytischen Funktionen einer oder mehrerer Komplexen Ver\u00e4nderlichen","volume":"112","author":"Cartan H.","year":"1966"},{"key":"rf3","first-page":"23","volume":"16","author":"Guzik G.","journal-title":"Wy\u017c. Szko\u0142a Ped. Krak\u00f3w Rocznik Nauk.-Dydact. Prace Matematyczne"},{"key":"rf4","first-page":"295","volume":"6","author":"Guzik G.","journal-title":"J. Appl. Anal."},{"key":"rf5","first-page":"31","volume":"344","author":"Guzik G.","journal-title":"Grazer Math. Berichte"},{"key":"rf6","series-title":"Power Series, Integration, Conformal Mapping, Location of Zeros","volume-title":"Applied and Computational Complex Analysis","author":"Henrici P.","year":"1974"},{"key":"rf7","series-title":"Monografie Mat.","volume-title":"Functional Equations in a Single Variable","volume":"46","author":"Kuczma M.","year":"1968"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139086639"},{"key":"rf9","first-page":"173","volume":"207","author":"Moszner Z.","journal-title":"Sitzungsberichte \u00d6AW, Math.-nat. Kl. Abt. II"},{"key":"rf10","first-page":"311","volume":"55","author":"Reich L.","journal-title":"Aequat. Math."},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1007\/BF01541637"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(70)90028-4"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127403007680","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T00:16:56Z","timestamp":1565137016000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127403007680"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,7]]},"references-count":12,"journal-issue":{"issue":"07","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2003,7]]}},"alternative-id":["10.1142\/S0218127403007680"],"URL":"https:\/\/doi.org\/10.1142\/s0218127403007680","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,7]]}}}