MATH 81400 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, 2nd expanded edition,
AMS, 2006.
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.
S. Krantz, Complex Analysis: The geometric viewpoint, 2nd edition, MAA, 2004.
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, 3rd edition, Princeton
University Press, 2006.
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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Math 81400