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.

Reçu le :
Accepté le :
Publié le :
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 
@article{CRMATH_2002__334_8_683_0,
     author = {Tsygvintsev, Alexei V. and Mestel, Ben D. and Osbaldestin, Andrew H.},
     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},
     url = {http://archive.numdam.org/articles/10.1016/S1631-073X(02)02330-0/}
}
TY  - JOUR
AU  - Tsygvintsev, Alexei V.
AU  - Mestel, Ben D.
AU  - Osbaldestin, Andrew H.
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
UR  - http://archive.numdam.org/articles/10.1016/S1631-073X(02)02330-0/
DO  - 10.1016/S1631-073X(02)02330-0
LA  - en
ID  - CRMATH_2002__334_8_683_0
ER  - 
%0 Journal Article
%A Tsygvintsev, Alexei V.
%A Mestel, Ben D.
%A Osbaldestin, Andrew H.
%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
%U http://archive.numdam.org/articles/10.1016/S1631-073X(02)02330-0/
%R 10.1016/S1631-073X(02)02330-0
%G en
%F CRMATH_2002__334_8_683_0
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://archive.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

Cité par Sources :