Continued fractions and solutions of the Feigenbaum–Cvitanović equation
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.

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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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Tsygvintsev, Alexei V.; Mestel, Ben D.; Osbaldestin, Andrew H. 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. 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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