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Book Review

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Book Information

Author(s): Curtis T. McMullen
Title: Complex dynamics and renormalization
Additional book information: Princeton University Press, 1994, vii + 214, $22.50, 0-691-02982-2 (cloth), 0-691-02981-4 (pbk)

Author(s): Curtis T. McMullen
Title: Renormalization and 3-manifolds which fiber over the circle
Additional book information: Princeton University Press, 1996, vii + 253, 0-691-01154-0 (cloth), 0-691-01153-2 (pbk)

References:

[DH1]
A. Douady & J.H. Hubbard. On the dynamics of polynomial-like maps. Ann. Sc. Éc. Norm. Sup., v. 18 (1985), 287-343. MR 87f:58083

[DH2]
A. Douady & J.H. Hubbard. A proof of Thurston's topological characterization of rational functions. Acta Math., v. 171 (1993), 263-297. MR 94j:58143

[F]
M.J. Feigenbaum. Quantitative universality for a class of non-linear transformations. J. Stat. Phys., v. 19 (1978), 25-52. MR 58:18601

[L1]
M. Lyubich. Dynamics of quadratic polynomials, I-II. Acta Math., v. 178 (1997), 185-297. MR 98e:58145

[L2]
M. Lyubich. Feigenbaum-Coullet-Tresser Universality and Milnor's Hairiness Conjecture. To appear in Ann. Math.

[MS]
W. de Melo & S. van Strien. One dimensional dynamics. Springer-Verlag, 1993. MR 95a:58035

[M]
J. Milnor. Self-similarity and hairiness in the Mandelbrot set, ``Computers in geometry and topology", Lect. Notes in Pure Appl Math, 114 (1989), 211-257. MR 90c:58086

[MT]
J. Milnor & W. Thurston. On iterated maps of the interval. ``Dynamical Systems", Proc. U. Md., 1986-87, ed. J. Alexander, Lect. Notes Math., v. 1342 (1988), 465-563. MR 90a:58083

[S1]
D. Sullivan. Quasiconformal homeomorphisms in dynamics, topology and geometry. Proc. ICM-86, Berkeley, v. II, Amer. Math. Soc., 1987, 1216-1228. MR 90a:58160

[S2]
D. Sullivan. Bounds, quadratic differentials, and renormalization conjectures. AMS Centennial Publications, 1992. 2: Mathematics into the Twenty-first Century (1992). MR 93k:58194

[TC]
C. Tresser & P. Coullet. Itération d'endomorphismes et groupe de renormalisation. C.R. Acad. Sc. Paris 287A (1978), 577-580. MR 80b:58043

Additional Information:

Reviewer(s):
Mikhail Lyubich
Email: mlyubich@math.sunysb.edu

Review Information:
Journal: Bull. Amer. Math. Soc. 36 (1999), 103-107.

MSC (1991): Primary 58F23
DOI: 10.1090/S0273-0979-99-00770-3
PII: S 0273-0979(99)00770-3
Copyright of article: Copyright 1999, American Mathematical Society

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