Continued fractions and solutions of the Feigenbaum–Cvitanović equation
[Fractions continues et des solutions de l'équation de Feigenbaum–Cvitanović]
Tsygvintsev, Alexei V.1 ; Mestel, Ben D.2 ; Osbaldestin, Andrew H.1
1 Department of Mathematical Sciences, Loughborough University, Loughborough, LE11 3TU, UK
2 School of Mathematical Sciences, University of Exeter, Exeter, EX4 4QE, UK
Comptes Rendus. Mathématique, Tome 334 (2002) no. 8, pp. 683-688.

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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Accepté le :
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DOI : 10.1016/S1631-073X(02)02330-0
Tsygvintsev, Alexei V. 1 ; Mestel, Ben D. 2 ; Osbaldestin, Andrew H. 1

1 Department of Mathematical Sciences, Loughborough University, Loughborough, LE11 3TU, UK
2 School of Mathematical Sciences, University of Exeter, Exeter, EX4 4QE, UK 
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     title = {Continued fractions and solutions of the {Feigenbaum{\textendash}Cvitanovi\'c} equation},
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Tsygvintsev, Alexei V.; Mestel, Ben D.; Osbaldestin, Andrew H. Continued fractions and solutions of the Feigenbaum–Cvitanović equation. Comptes Rendus. Mathématique, Tome 334 (2002) no. 8, pp. 683-688. doi : 10.1016/S1631-073X(02)02330-0. http://www.numdam.org/articles/10.1016/S1631-073X(02)02330-0/

[1] Donoghue, W.F. Monotone Matrix Functions and Analytic Continuation, Grundlehren Math. Wiss., 207, Springer-Verlag, New York, 1974

[2] Epstein, H. New proofs of the existence of the Feigenbaum functions, Comm. Math. Phys., Volume 106 (1986) no. 3, pp. 395-426

[3] Epstein, H. Fixed points of composition operators, Procceedings of a NATO Advanced Study Institute on Nonlilenar Evolution, Italy, 1987, pp. 71-100

[4] Epstein, H.; Lascoux, J. Analyticity properties of the Feigenbaum function, Comm. Math. Phys., Volume 81 (1981), pp. 437-453

[5] Wall, H.S. Analytic Theory of Continued Fractions, Van Nostrand, New York, NY, 1948

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