[Fractions continues et des solutions de l'équation de Feigenbaum–Cvitanović]
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.
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.
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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/
[1] Monotone Matrix Functions and Analytic Continuation, Grundlehren Math. Wiss., 207, Springer-Verlag, New York, 1974
[2] New proofs of the existence of the Feigenbaum functions, Comm. Math. Phys., Volume 106 (1986) no. 3, pp. 395-426
[3] Fixed points of composition operators, Procceedings of a NATO Advanced Study Institute on Nonlilenar Evolution, Italy, 1987, pp. 71-100
[4] Analyticity properties of the Feigenbaum function, Comm. Math. Phys., Volume 81 (1981), pp. 437-453
[5] Analytic Theory of Continued Fractions, Van Nostrand, New York, NY, 1948
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