[1]Brück, R.. Geometric properties of Julia sets of the composition of polynomials of the form *z* ^{2}+*c* _{n}. Pacific J. Math. 198(2) (2001), 347–372.

[2]Brück, R., Büger, M. and Reitz, S.. Random iterations of polynomials of the form *z* ^{2}+*c* _{n}: Connectedness of Julia sets. Ergod. Th. & Dynam. Sys. 19(5) (1999), 1221–1231.

[3]Büger, M.. Self-similarity of Julia sets of the composition of polynomials. Ergod. Th. & Dynam. Sys. 17 (1997), 1289–1297.

[4]Büger, M.. On the composition of polynomials of the form *z* ^{2}+*cn*. Math. Ann. 310(4) (1998), 661–683.

[5]Fornaess, J. E. and Sibony, N.. Random iterations of rational functions. Ergod. Th. & Dynam. Sys. 11 (1991), 687–708.

[6]Gong, Z. and Qiu, W.. Connectedness of Julia sets for a quadratic random dynamical system. Ergod. Th. & Dynam. Sys. 23 (2003), 1807–1815.

[7]Gong, Z. and Ren, F.. A random dynamical system formed by infinitely many functions. J. Fudan University 35 (1996), 387–392.

[8]Hinkkanen, A. and Martin, G. J.. The dynamics of semigroups of rational functions I. Proc. London Math. Soc. (3) 73 (1996), 358–384.

[9]Hinkkanen, A. and Martin, G. J.. Julia Sets of Rational Semigroups. Math. Z. 222(2) (1996), 161–169.

[10]Kato, T.. Perturbation Theory for Linear Operators. Springer, Berlin, 1995.

[11]Klimek, M.. Pluripotential Theory *(London Mathematical Society Monographs, New Series, 6)*. Oxford Science Publications/The Clarendon Press/Oxford University Press, New York, 1991.

[12]Mauldin, D. and Urbański, M.. Graph Directed Markov Systems: Geometry and Dynamics of Limit Sets. Cambridge University Press, Cambridge, 2003.

[13]McMullen, C.. Complex Dynamics and Renormalization *(Annals of Mathematics Studies, 135)*. Princeton University Press, Princeton, NJ, 1994.

[14]Milnor, J.. Dynamics in One Complex Variable, 3rd edn*(Annals of Mathematical Studies, 160)*. Princeton University Press, Princeton, NJ, 2006.

[16]Ruelle, D.. Repellers for real-analytic maps. Ergod. Th. & Dynam. Sys. 2 (1982), 99–107.

[17]Stankewitz, R.. Completely invariant Julia sets of polynomial semigroups. Proc. Amer. Math. Soc. 127(10) (1999), 2889–2898.

[18]Stankewitz, R.. Completely invariant sets of normality for rational semigroups. Complex Variables Theory Appl. 40 (2000), 199–210.

[19]Stankewitz, R.. Uniformly perfect sets rational semigroups, Kleinian groups and IFS’s. Proc. Amer. Math. Soc. 128(9) (2000), 2569–2575.

[20]Stankewitz, R., Sugawa, T. and Sumi, H.. Some counterexamples in dynamics of rational semigroups. Ann. Acad. Sci. Fenn. Math. 2(9) (2004), 357–366.

[21]Stankewitz, R. and Sumi, H.. Dynamical properties and structure of Julia sets of postcritically bounded polynomial semigroups. *Preprint*, 2008, http://arxiv.org/abs/0708.3187. [22]Sumi, H.. On dynamics of hyperbolic rational semigroups. J. Math. Kyoto Univ. 37(4) (1997), 717–733.

[23]Sumi, H.. On Hausdorff dimension of Julia sets of hyperbolic rational semigroups. Kodai Math. J. 21(1) (1998), 10–28.

[24]Sumi, H.. Skew product maps related to finitely generated rational semigroups. Nonlinearity 13 (2000), 995–1019.

[25]Sumi, H.. Dynamics of sub-hyperbolic and semi-hyperbolic rational semigroups and skew products. Ergod. Th. & Dynam. Sys. 21 (2001), 563–603.

[26]Sumi, H.. A correction to the proof of a lemma in ‘Dynamics of sub-hyperbolic and semi-hyperbolic rational semigroups and skew products. Ergod. Th. & Dynam. Sys. 21 (2001), 1275–1276.

[28]Sumi, H.. Semi-hyperbolic fibered rational maps and rational semigroups. Ergod. Th. & Dynam. Sys. 26 (2006), 893–922.

[29]Sumi, H.. Random dynamics of polynomials and devil’s-staircase-like functions in the complex plane. Appl. Math. Comput. 187 (2007), 489–500 (Proceedings paper).

[30]Sumi, H.. The space of postcritically bounded 2-generator polynomial semigroups with hyperbolicity, *RIMS Kokyuroku* 1494, 2006, pp. 62–86 (Proceedings paper).

[31]Sumi, H.. Dynamics of postcritically bounded polynomial semigroups I: connected components of the Julia sets. *Preprint*, 2008, http://arxiv.org/abs/0811.3664. [32]Sumi, H.. Dynamics of postcritically bounded polynomial semigroups III: classification of semi-hyperbolic semigroups and random Julia sets which are Jordan curves but not quasicircles. *Preprint*, 2008, http://arxiv.org/abs/0811.4536. [36]Sumi, H.. In preparation.

[37]Sumi, H. and Urbański, M.. The equilibrium states for semigroups of rational maps, *Monatsh. Math.* to appear, available at http://arxiv.org/abs/0707.2444. [38]Sumi, H. and Urbański, M.. Measures and dimensions of Julia sets of semi-hyperbolic rational semigroups. *Preprint*, 2008, http://arxiv.org/abs/0811.1809. [39]Sumi, H. and Urbański, M.. In preparation.

[40]Urbański, M. and Zdunik, A.. Real analyticity of Hausdorff dimension of finer Julia sets of exponential family. Ergod. Th. & Dynam. Sys. 24 (2004), 279–315.

[41]Zhou, W. and Ren, F.. The Julia sets of the random iteration of rational functions. Chinese Sci. Bull. 37(12) (1992), 969–971.

[42]Zinsmeister, M.. Thermodynamic Formalism and Holomorphic Dynamical Systems. American Mathematical Society, Providence, RI, 2000.