MAT 748 References

Background in complex analysis and quasiconformal theory:

L. Ahlfors, Conformal invariants: topics in geometric function theory, McGraw-Hill, 1973.

L. Ahlfors, Lectures on quasiconformal mappings, Van Nostrand, 1966.

L. Bers, Quasiconformal mappings, with applications to differential equations, function theory and topology, Bull. Amer. Math. Soc. 83 (1977) 1083-1100.

Y. Imayoshi and M. Taniguchi, An introduction to Teichmuller spaces, Springer-Verlag, 1992.

O. Lehto, Univalent functions and Teichmuller spaces, Graduate Texts in Mathematics 109, Springer-Verlag, 1987.

O. Lehto and K. Virtanen, Quasiconformal mappings in the plane, 2nd edition, Springer-Verlag, 1973.

Books and surverys in complex dynamics:

A. Beardon, The Iteration of Rational Functions: Complex Analytic Dynamical Systems, Springer-Verlag, 1991.

P. Blanchard, Complex analytic dynamics on the Riemann sphere, Bull. Amer. Math. Soc. (N.S.) 11 (1984) 85-141.

L. Carleson and T. Gamelin, Complex Dynamics, Springer-Verlag, 1993.

A. Erkmenko and M. Lyubich, The dynamics of analytic transformations, Leningrad Math. J. 1 (1990) 563-634.

M. Lyubich, The dynamics of rational transforms: the topological picture, Russian Math Surveys 41:4 (1986) 43-117.

C. McMullen, Frontiers in complex dynamics, Bull. Amer. Math. Soc. (N.S.) 31 (1994) 155-172.

C. McMullen, Complex Dynamics and Renormalization, Annals of Math Studies 135, Princeton University Press, 1996.

J. Milnor, Dynamics in One Complex Variable: Introductory Lectures, Vieweg, 1999.

N. Steinmetz, Rational Iteration : Complex Analytic Dynamical Systems, Walter de Gruyter, 1993.

Papers:

L. Bers and H. Royden, Holomorphic families of injections, Acta Math. 157 (1986) 259-286.

B. Branner, The Mandelbrot set, in Chaos and fractals pp. 75-105, Proc. Sympos. Appl. Math., 39, Amer. Math. Soc., 1989.

R. Mane, P. Sad and D. Sullivan, On the dynamics of rational maps, Ann. Sci. Ecole Norm. Sup. (4) 16 (1983) 193-217.

C. McMullen and D. Sullivan, Quasiconformal homeomorphisms and dynamics III: The Teichmuller space of a holomorphic dynamical system, Adv. Math 135 (1998) 351-395.

Z. Slodkowski, Holomorphic motions and polynomial hulls, Proc. Amer. Math. Soc. 111 (1991) 347-355.

D. Sullivan, Quasiconformal homeomorphisms and dynamics I: Solution of the Fatou-Julia problem on wandering domains, Annals of Math. 122 (1985) 401-418.

D. Sullivan and W. Thurston, Extending holomorphic motions Acta Math. 157 (1986) 243-257.

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