@article{PMIHES_1997__85__193_0,
author = {Hill, Richard and Velani, Sanju L.},
title = {Metric diophantine approximation in {Julia} sets of expanding rational maps},
journal = {Publications Math\'ematiques de l'IH\'ES},
pages = {193--216},
publisher = {Institut des Hautes \'Etudes Scientifiques},
volume = {85},
year = {1997},
mrnumber = {1471868},
zbl = {0885.11051},
language = {en},
url = {http://archive.numdam.org/item/PMIHES_1997__85__193_0/}
}
TY - JOUR AU - Hill, Richard AU - Velani, Sanju L. TI - Metric diophantine approximation in Julia sets of expanding rational maps JO - Publications Mathématiques de l'IHÉS PY - 1997 SP - 193 EP - 216 VL - 85 PB - Institut des Hautes Études Scientifiques UR - http://archive.numdam.org/item/PMIHES_1997__85__193_0/ LA - en ID - PMIHES_1997__85__193_0 ER -
%0 Journal Article %A Hill, Richard %A Velani, Sanju L. %T Metric diophantine approximation in Julia sets of expanding rational maps %J Publications Mathématiques de l'IHÉS %D 1997 %P 193-216 %V 85 %I Institut des Hautes Études Scientifiques %U http://archive.numdam.org/item/PMIHES_1997__85__193_0/ %G en %F PMIHES_1997__85__193_0
Hill, Richard; Velani, Sanju L. Metric diophantine approximation in Julia sets of expanding rational maps. Publications Mathématiques de l'IHÉS, Tome 85 (1997), pp. 193-216. http://archive.numdam.org/item/PMIHES_1997__85__193_0/
[1] , Iteration of Rational Functions, Springer GTM 132, 1991. | MR | Zbl
[2] , Sets of fractional dimension (IV): On rational approximation to real numbers, J. London Math. Soc. 9 (1934), 126-131. | JFM | Zbl
[3] , Equilibrium States and the Ergodic Theory for Anosov Diffeomorphisms, III, Springer LNM 470, 1975. | MR | Zbl
[4] , Invariant sets under iteration of rational functions, Ark. Mat. 6 (1965), 103-144. | MR | Zbl
[5] , An Introduction to Diophantine Approximation, Cambridge Univ. Press, 1957. | MR | Zbl
[6] , and , Ergodic Theory on Compact Spaces, IV, Springer LNM 527, 1976. | MR | Zbl
[7] and , Ergodic theory of equilibrium states of rational maps, Nonlinearity 4 (1991), 103-134. | MR | Zbl
[8] , Fractal Geometry - Mathematical Foundations and Applications, J. Wiley, Chichester, 1990. | Zbl
[9] and , The Ergodic Theory of Shrinking Targets, Invent. Math. 119 (1995), 175-198. | MR | Zbl
[10] and , Markov maps and moving, shrinking targets, in preparation.
[11] and , The Shrinking Target Problem for Matrix Transformations of Tori, J. Lond. Math. Soc. (to appear). | Zbl
[12] and , The Jarník-Besicovitch theorem for geometrically finite Kleinian groups, Proc. Lond. Math. Soc. (to appear). | Zbl
[13] , Analytic function theory, Ginn and Company: Boston - New York - Chicago - Atlanta - Dallas - Palo Alto - Toronto, 1962. | MR | Zbl
[14] , Diophantische Approximationen und Hausdorffsches Mass, Math. Sb. 36 (1929), 371-382. | JFM
[15] , Entropy properties of rational endomorphisms of the Riemann sphere, Ergod. Th. Dynam. Sys. 3 (1983), 351-386. | MR | Zbl
[16] and , Geodesic excursions into cusps in infinite volume hyperbolic manifolds, Mathematica Gottingensis 45, 1993. | Zbl
[17] and , Zeta functions and the periodic orbit structure of hyperbolic dynamics, Astérisque, Soc. Math. France, 187-188, 1990. | Numdam | MR | Zbl
[18] , The limit set of a Fuchsian group, Acta Math. 136 (1976), 241-273. | MR | Zbl
[19] , Thermodynamical Formalism, Encycl. Math. Appl. 5, 1978. | MR | Zbl
[20] , Metric theory of Diophantine approximation (translated by R. A. SILVERMAN), V. H. Winston & Sons, Washington D.C., 1979. | MR
[21] , Conformal Dynamical Systems, in Proc. Conf. on Geometric Dynamics, Rio de Janeiro, 1981, Springer LNM 1007, 725-752. | MR | Zbl
[22] , A variational principle for the pressure of continuous transformations, Am. J. Math. 97 (1975), 937-971. | MR | Zbl
