Multifractal analysis of nearly circular Julia set and thermodynamical formalism
Annales de l'I.H.P. Physique théorique, Tome 56 (1992) no. 1, pp. 91-122. 
@article{AIHPA_1992__56_1_91_0,
     author = {Collet, P. and Dobbertin, R. and Moussa, P.},
     title = {Multifractal analysis of nearly circular {Julia} set and thermodynamical formalism},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     pages = {91--122},
     publisher = {Gauthier-Villars},
     volume = {56},
     number = {1},
     year = {1992},
     mrnumber = {1149870},
     zbl = {0759.58033},
     language = {en},
     url = {http://www.numdam.org/item/AIHPA_1992__56_1_91_0/}
}
TY  - JOUR
AU  - Collet, P.
AU  - Dobbertin, R.
AU  - Moussa, P.
TI  - Multifractal analysis of nearly circular Julia set and thermodynamical formalism
JO  - Annales de l'I.H.P. Physique théorique
PY  - 1992
SP  - 91
EP  - 122
VL  - 56
IS  - 1
PB  - Gauthier-Villars
UR  - http://www.numdam.org/item/AIHPA_1992__56_1_91_0/
LA  - en
ID  - AIHPA_1992__56_1_91_0
ER  - 
%0 Journal Article
%A Collet, P.
%A Dobbertin, R.
%A Moussa, P.
%T Multifractal analysis of nearly circular Julia set and thermodynamical formalism
%J Annales de l'I.H.P. Physique théorique
%D 1992
%P 91-122
%V 56
%N 1
%I Gauthier-Villars
%U http://www.numdam.org/item/AIHPA_1992__56_1_91_0/
%G en
%F AIHPA_1992__56_1_91_0
Collet, P.; Dobbertin, R.; Moussa, P. Multifractal analysis of nearly circular Julia set and thermodynamical formalism. Annales de l'I.H.P. Physique théorique, Tome 56 (1992) no. 1, pp. 91-122. http://www.numdam.org/item/AIHPA_1992__56_1_91_0/

[1] M.H. Jensen, L.P. Kadanoff, A. Libchaber, I. Procaccia and J. Stavans, Phys. Rev. Lett., Vol. 55, 1985, pp. 2798-2801.

[2] T.C. Halsey, M.H. Jensen, L.P. Kadanoff, I. Procaccia and B.I. Shraiman, Phys. Rev., Vol. A 33, 1986, pp. 1141-1151.

[3] M.J. Feigenbaum, J. Stat. Phys., Vol. 46, 1987, pp. 919-924. | Zbl

[4] M.J. Feigenbaum, M.H. Jensen and I. Procaccia, Phys. Rev. Lett., Vol. 57, 1986, pp. 1503-1506. | MR

[5] H.G.E. Hentschel and I. Procaccia, Physica, Vol. 8D, 1983, pp. 435-444. | MR | Zbl

[6] P. Grassberger and I. Procaccia, Physica, Vol. 13 D, 1984, pp. 34-54. | MR | Zbl

[7] R. Badii and A. Politi, J. Stat. Phys., Vol. 40, 1985, pp. 725-750. | MR | Zbl

[8] G. Paladin and A. Vulpiani, Lett. Nuovo Cim., Vol. 41, 1984, pp. 82-86; R. Benzi, G. Paladin, G. Parisi and A. Vulpiani, J. Phys. A: Math. Gen., Vol. 17, 1984, p. 3521-3531. | MR

[9] B.B. Mandelbrot, J. Fluid Mech., Vol. 62, 1974, pp. 331-358. | Zbl

[10] T. Bohr and D. Rand, Physica, Vol. 25 D, 1987, pp. 387-398, D. Rand, Ergod. Theor. Dynam. Sys., Vol. 9, 1989, pp. 527-541. | MR | Zbl

[11] T. Bohr and T. Tel, The Thermodynamic of Fractals, in: Directions in Chaos, HAO BAI LIN Ed., World Scientific, Singapore, 1988, Vol. 2, pp. 194-237; T. Tel, Zeitschrift für Naturforschung, Vol. 43 a, 1988, pp. 1-72.

[12] G. Servizi, G. Turchetti and S. Vaienti, J. Phys. A: Math. Gen., Vol. 21, 1988, L 639-L 643. | MR

[13] S. Vaienti, J. Phys. A: Math. Gen., Vol. 21, 1988, pp. 2023-2043. | Zbl

[14] J.P. Eckmann and I. Procaccia, Phys. Rev., Vol. A 34, 1986, pp. 659-661.

[15] O.E. Lanford, Entropy and equilibrium states in classical statistical mechanics, in: Statistical Mechanics and Mathematical Problems, A. LENARD Ed., Lecture Note in Physics, Vol. 20, pp. 1-113, Springer 1973.

[16] P. Collet, J.L. Lebowitz and A. Porzio, J. Stat. Phys., Vol. 47, 1987, pp. 609-644. | MR | Zbl

[17] P. Blanchard, Bull. Am. Math. Soc., Vol. 11, 1984, pp. 85-141. | MR | Zbl

[18] D. Ruelle Ergod. Theor. Dynam. Sys., Vol. 2, 1982, pp. 99-107. | Zbl

[19] M. Widom, D. Bensimon, L.P. Kadanoff and S.J. Shenker, J. Stat. Phys., Vol. 32, 1983, pp. 443-454. | MR | Zbl

[20] P. Collet, Hausdorff dimension of the singularities for invariant measures of expanding dynamical system in Dynamical Systems, Valparaiso 1986, R. BAMÒN, R. LABARCA and J. PALIS Eds., Lecture Notes in Mathematics, Vol. 1331, pp. 47-58, Springer 1988. | MR | Zbl

[21] P. Moussa Hausdorff Dimension and Dimension Spectrum for Julia Sets Close to Unit Circle, in: Non Linear Dynamics, G. TURCHETTI Ed., World Scientific, Singapore, pp. 88-108, 1989; P. Moussa, Grandes déviations et analyse des objets fractals, in: Comptes Rendus des Rencontres entre Physiciens Théoriciens et Mathématiciens, R.C.P. 25, Vol. 41, pp. 131-142, Publ. de l'I.R.M.A., Université de Strasbourg, 1990. | Zbl

[22] H. Brolin, Ark. Mat., Vol. 6, 1965, pp. 103-144. | MR | Zbl

[23] M.F. Barnsley, J.S. Geronimo and A.N. Harrington, Bull. Am. Math. Soc., Vol. 7, 1982, pp. 381-384. | MR | Zbl

[24] D. Sullivan, Seminar on Conformal and Hyperbolic Geometry, I.H.E.S. Preprint, Bures-sur-Yvette, France, 1982.

[25] R.S. Ellis, Entropy, Large Deviations and Statistical Mechanics, Springer, New York, 1985. | MR | Zbl

[26] S.R.S. Varadhan, Large Deviations and Applications, S.I.A.M. Regional Conference Series in Applied Mathematics, Vol. 46, 1984, see also: Grandes Déviations et Applications Statistiques, Séminaire, Faculté des Sciences d'Orsay, 1977-1978, Astérisque, Vol. 68, 1978. | MR

[27] D. Plachky, Ann. Math. Stat., Vol. 42, 1971, pp. 1442-1443. | MR | Zbl

[28] D. Plachky and J. Steinebach, Period. Math., Vol. 6, 1974, pp. 338-340.

[29] D. Katzen and I. Procaccia, Phys. Rev. Lett., Vol. 58, 1987, pp. 1169-1172. | MR

[30] R. Badii and A. Politi, Phase Transitions in Hyperbolic Dynamical Systems, in: Chaos and Complexity, R. LIVI, S. RUFFO, S. CILIBERTO and M. BUIATTI Eds., World Scientific, Singapore, 1988, pp. 42-48; R. Badii, Rivista del Nuov. Cim., Vol. 12, No. 3, 1989, pp. 1-72. | MR | Zbl

[31] K.J. Falconer, The Geometry of Fractal Sets, Cambridge University Press, 1985. | MR | Zbl

[32] O. Frostman, Ann. Univ. Lund, 1935.

[33] J.P. Kahane, Ensembles Aléatoires et Dimensions, in: Recent Progress in Fourier Analysis, I. PERAL and J. L. RUBIO DE FRANCIA Ed., Elsevier North Holland, 1985. | MR | Zbl

[34] R.L. Dobrushin, Induction on Volume and No Cluster Expansion, in VIIIth International Congress On Mathematical Physics, M. MEBKHOUT and R. SENEOR Eds., World Scientific, Singapore, 1987, pp. 73-91. | MR

[35] R. Bowen, Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms, Lecture Notes in Mathematics, Springer Verlag, Berlin, Vol. 470, 1975. | MR | Zbl

[36] D. Ruelle, Thermodynamic formalism, Addison Wesley, Reading, 1978. | MR

[37] E. Vul, K. Khanin and Y. Sinai, Russ. Math. Surv., Vol. 39, 1984, pp. 1-40. | MR | Zbl

[38] G. Paladin and A. Vulpiani, Physics Reports, Vol. 156, 1987, pp. 147-225. | MR

[39] P. Billingsley, Ergodic Theory and Information, John Wiley & Sons, New York 1965, pp. 136-145. | Zbl

[40] A. Porzio, J. Stat. Phys., Vol. 58, 1990, pp. 923-937. | Zbl

[41] G. Brown, G. Michon and J. Peyrière, On the Multifractal Analysis of Measures preprint, 1990.