@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] Phys. Rev. Lett., Vol. 55, 1985, pp. 2798-2801.
, , , and ,[2] Phys. Rev., Vol. A 33, 1986, pp. 1141-1151.
, , , and ,[3] J. Stat. Phys., Vol. 46, 1987, pp. 919-924. | Zbl
,[4] Phys. Rev. Lett., Vol. 57, 1986, pp. 1503-1506. | MR
, and ,[5] Physica, Vol. 8D, 1983, pp. 435-444. | MR | Zbl
and ,[6] Physica, Vol. 13 D, 1984, pp. 34-54. | MR | Zbl
and ,[7] J. Stat. Phys., Vol. 40, 1985, pp. 725-750. | MR | Zbl
and ,[8] Lett. Nuovo Cim., Vol. 41, 1984, pp. 82-86; , , and , J. Phys. A: Math. Gen., Vol. 17, 1984, p. 3521-3531. | MR
and ,[9] J. Fluid Mech., Vol. 62, 1974, pp. 331-358. | Zbl
,[10] Physica, Vol. 25 D, 1987, pp. 387-398, , Ergod. Theor. Dynam. Sys., Vol. 9, 1989, pp. 527-541. | MR | Zbl
and ,[11] The Thermodynamic of Fractals, in: Directions in Chaos, HAO BAI LIN Ed., World Scientific, Singapore, 1988, Vol. 2, pp. 194-237; , Zeitschrift für Naturforschung, Vol. 43 a, 1988, pp. 1-72.
and ,[12] J. Phys. A: Math. Gen., Vol. 21, 1988, L 639-L 643. | MR
, and ,[13] J. Phys. A: Math. Gen., Vol. 21, 1988, pp. 2023-2043. | Zbl
,[14] Phys. Rev., Vol. A 34, 1986, pp. 659-661.
and ,[15] 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] J. Stat. Phys., Vol. 47, 1987, pp. 609-644. | MR | Zbl
, and ,[17] Bull. Am. Math. Soc., Vol. 11, 1984, pp. 85-141. | MR | Zbl
,[18] Ergod. Theor. Dynam. Sys., Vol. 2, 1982, pp. 99-107. | Zbl
[19] J. Stat. Phys., Vol. 32, 1983, pp. 443-454. | MR | Zbl
, , and ,[20] 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] 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; , 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] Ark. Mat., Vol. 6, 1965, pp. 103-144. | MR | Zbl
,[23] Bull. Am. Math. Soc., Vol. 7, 1982, pp. 381-384. | MR | Zbl
, and ,[24] Seminar on Conformal and Hyperbolic Geometry, I.H.E.S. Preprint, Bures-sur-Yvette, France, 1982.
,[25] Entropy, Large Deviations and Statistical Mechanics, Springer, New York, 1985. | MR | Zbl
,[26] 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] Ann. Math. Stat., Vol. 42, 1971, pp. 1442-1443. | MR | Zbl
,[28] Period. Math., Vol. 6, 1974, pp. 338-340.
and ,[29] Phys. Rev. Lett., Vol. 58, 1987, pp. 1169-1172. | MR
and ,[30] 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; , Rivista del Nuov. Cim., Vol. 12, No. 3, 1989, pp. 1-72. | MR | Zbl
and ,[31] The Geometry of Fractal Sets, Cambridge University Press, 1985. | MR | Zbl
,[32] Ann. Univ. Lund, 1935.
,[33] 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] 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] Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms, Lecture Notes in Mathematics, Springer Verlag, Berlin, Vol. 470, 1975. | MR | Zbl
,[36] Thermodynamic formalism, Addison Wesley, Reading, 1978. | MR
,[37] Russ. Math. Surv., Vol. 39, 1984, pp. 1-40. | MR | Zbl
, and ,[38] Physics Reports, Vol. 156, 1987, pp. 147-225. | MR
and ,[39] Ergodic Theory and Information, John Wiley & Sons, New York 1965, pp. 136-145. | Zbl
,[40] J. Stat. Phys., Vol. 58, 1990, pp. 923-937. | Zbl
,[41] On the Multifractal Analysis of Measures preprint, 1990.
, and ,