Itération des polynômes et propriétés d'orthogonalité
Annales de l'I.H.P. Physique théorique, Volume 44 (1986) no. 3, p. 315-325
@article{AIHPA_1986__44_3_315_0,
     author = {Moussa, Pierre},
     title = {It\'eration des polyn\^omes et propri\'et\'es d'orthogonalit\'e},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     publisher = {Gauthier-Villars},
     volume = {44},
     number = {3},
     year = {1986},
     pages = {315-325},
     zbl = {0607.30024},
     mrnumber = {846471},
     language = {fr},
     url = {http://www.numdam.org/item/AIHPA_1986__44_3_315_0}
}
Moussa, Pierre. Itération des polynômes et propriétés d'orthogonalité. Annales de l'I.H.P. Physique théorique, Volume 44 (1986) no. 3, pp. 315-325. http://www.numdam.org/item/AIHPA_1986__44_3_315_0/

[1] G. Julia, Mémoire sur l'itération des fonctions rationnelles. J. Math. Pur. Appl., t. 7, 1918, p. 503-529; P. Fatou, Sur les équations fonctionnelles, Bull. Soc. Math. France, t. 47, 1919, p. 161-271; t. 48, 1920, p. 33-94, t. 48, 1920, p. 208- 314. | JFM 46.0520.06 | MR 1504792

[2] B. Mandelbrot, Fractal aspects of the iteration of z → λz(1 - z) for complex λ and z, Annals N. Y. Acad. Sci., t. 357, 1980, p. 249-259; On the quadratic mapping z → z2 - μ for complex μ and z, the fractal structure of its M set, and scaling, Physica, t. 7D, 1983, p. 224-239. | MR 719054 | Zbl 1194.30028 | Zbl 0478.58017

[3] D. Sullivan, Itération des fonctions analytiques complexes, C. R. Acad. Sci., Paris, Sér. I, t. 294, 1982, p. 301-303 ; Quasi conformal homeomorphisms and dynamics I, II, III, preprint IHES, 1982-1983. | MR 658395 | Zbl 0496.30016

[4] A Douady, J.H. Hubbard, Itération des polynômes quadratiques complexes, C. R. Acad. Sci. Paris, Sér. I, t. 294, 1982, 123-126; A. Douady, Systèmes dynamiques holomorphes. Séminaire Bourbaki, n° 599, Astérisque, t. 105-106, 1983, p. 39-63. | Numdam | MR 651802 | Zbl 0483.30014

[5] P. Blanchard, Complex analytical dynamics on the Riemann sphere, Bull. Amer. Math. Soc. t. 11, 1984, p. 85-141. | MR 741725 | Zbl 0558.58017

[6] H. Brolin, Invariant sets under iteration of rational functions, Ark. Mat., t. 6, 1965, p. 103-144; M.J. Ljubich, Entropy properties of rational endomorphisms of the Riemann sphere, Ergod. Th. Dynam. Syst., t. 3, 1983, p. 351-385. | MR 741393 | MR 194595 | Zbl 0127.03401

[7] D. Bessis, M.L. Mehta, P. Moussa, Polynômes orthogonaux sur des ensembles de Cantor et itérations des transformations quadratiques, C. R. Acad. Sci, Paris, Sér. I, t. 293, 1981, p. 705-708. | MR 650541 | Zbl 0493.33014

[8] D. Bessis, M.L. Mehta, P. Moussa, Orthogonal polynomials on a family of Cantor sets and the problem of iterations of quadratic mappings, Lett. Math. Phys., t. 6, 1982, p. 123-140. | MR 651127 | Zbl 0483.33006

[9] D. Bessis, P. Moussa, Orthogonality properties of iterated polynomial mappings, Comm. Math. Phys., t. 88, 1983, p. 503-529. | MR 702566 | Zbl 0523.30019

[10] J. Bellissard, D. Bessis, P. Moussa, Chaotic states of almost periodic Schrôdinger operators, Phys. Rev. Lett., t. 49, 1982, p. 701-704. | MR 669364

[11] G. Baker, D. Bessis, P. Moussa, A family of almost periodic Schrôdinger operators, Physica, t. 124A, 1984, p. 61-78. | MR 759169 | Zbl 0598.47054

[12] M. Barnsley, J. Geronimo, A. Harrington, On the invariant sets of a family of quadratic maps. Commun. Math. Phys., t. 88, 1983, p. 479-501. | MR 702565 | Zbl 0535.30024

[13] M. Barnsley, J. Geronimo, A. Harrington, Orthogonal polynomials associated with invariant measures on Julia sets, Bull. Amer. Math. Soc., t. 7, 1982, p. 381-384. | MR 663789 | Zbl 0509.30023

[14] M. Barnsley, J. Geronimo, A. Harrington, Infinite dimensional Jacobi matrices associated with Julia sets, Proc. Amer. Math. Soc., t. 88, 1983, p. 625-630. | MR 702288 | Zbl 0535.30025

[15] M. Barnsley, J. Geronimo, A. Harrington, Geometry, electrostatic measures and orthogonal polynomials on Julia sets for polynomials, Ergod. Th. Dynam. Sys., t. 3, 1983, p. 509-520. | MR 753919 | Zbl 0566.41033

[16] G. Szego, Orthogonal Polynomials, Amer. Math. Soc. Colloquium Publ., t. 23, 1939. | JFM 65.0278.03 | Zbl 0023.21505

[17] G.A. Baker, Essentials of Pade Approximants, Academic Press, N. Y., 1975. | Zbl 0315.41014

[18] T. Pitcher, J. Kinney, Some connections between ergodic theory and the iteration of polynomials, Ark, Mat., t. 8, 1968, p. 25-32. | MR 263125 | Zbl 0195.35501

[19] D. Bessis, J. Geronimo, P. Moussa, Mellin transforms associated with Julia sets and physical applications, J. Stat. Phys., t. 34, 1984, p. 75-110; Complex spectral dimensionality on fractal structures, J. Physique Lettres, t. 44, 1983, p. L977- L982. | MR 739123 | Zbl 0602.58028

[20] P. Moussa, Un opérateur de Schrôdinger presque périodique à spectre singulier associé aux itérations d'un polynôme, Comptes Rendus de la RCP 25 du CNRS, t. 34, 1984, p. 43-66, Publ. IRMA, Strasbourg.