Comptes Rendus
no. 8
Continued fractions and solutions of the Feigenbaum–Cvitanović equation
[Fractions continues et des solutions de l'équation de Feigenbaum–Cvitanović]
Alexei V. Tsygvintsev1 ; Ben D. Mestel2 ; Andrew H. Osbaldestin1
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, Volume 334 (2002) no. 8, pp. 683-688.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(02)02330-0

Alexei V. Tsygvintsev 1 ; Ben D. Mestel 2 ; Andrew H. Osbaldestin 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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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] W.F. Donoghue Monotone Matrix Functions and Analytic Continuation, Grundlehren Math. Wiss., 207, Springer-Verlag, New York, 1974

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

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

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

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

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