In this paper, we develop a new approach to the construction of solutions of the Feigenbaum–Cvitanović equation whose existence was shown by H. Epstein. Our main tool is the analytic theory of continued fractions.
Dans ce travail, nous énonçons une nouvelle méthode de construction des solutions de l'équation de Feigenbaum–Cvitanović dont l'existence a été montrée par H. Epstein. On utilise la théorie analytique des fractions continues.
Accepted:
Published online:
Alexei V. Tsygvintsev 1; Ben D. Mestel 2; Andrew H. Osbaldestin 1
@article{CRMATH_2002__334_8_683_0, author = {Alexei V. Tsygvintsev and Ben D. Mestel and Andrew H. Osbaldestin}, title = {Continued fractions and solutions of the {Feigenbaum{\textendash}Cvitanovi\'c} equation}, journal = {Comptes Rendus. Math\'ematique}, pages = {683--688}, publisher = {Elsevier}, volume = {334}, number = {8}, year = {2002}, doi = {10.1016/S1631-073X(02)02330-0}, language = {en}, }
TY - JOUR AU - Alexei V. Tsygvintsev AU - Ben D. Mestel AU - Andrew H. Osbaldestin TI - Continued fractions and solutions of the Feigenbaum–Cvitanović equation JO - Comptes Rendus. Mathématique PY - 2002 SP - 683 EP - 688 VL - 334 IS - 8 PB - Elsevier DO - 10.1016/S1631-073X(02)02330-0 LA - en ID - CRMATH_2002__334_8_683_0 ER -
%0 Journal Article %A Alexei V. Tsygvintsev %A Ben D. Mestel %A Andrew H. Osbaldestin %T Continued fractions and solutions of the Feigenbaum–Cvitanović equation %J Comptes Rendus. Mathématique %D 2002 %P 683-688 %V 334 %N 8 %I Elsevier %R 10.1016/S1631-073X(02)02330-0 %G en %F CRMATH_2002__334_8_683_0
Alexei V. Tsygvintsev; Ben D. Mestel; Andrew H. Osbaldestin. Continued fractions and solutions of the Feigenbaum–Cvitanović equation. Comptes Rendus. Mathématique, Volume 334 (2002) no. 8, pp. 683-688. doi : 10.1016/S1631-073X(02)02330-0. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02330-0/
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[5] Analytic Theory of Continued Fractions, Van Nostrand, New York, NY, 1948
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