Book Review
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Book Information:
Author: Curtis T. McMullen
Title: Complex dynamics and renormalization
Additional book information: Princeton University Press, 1994, vii + 214 pp., $22.50; ISBN 0-691-02982-2, cloth; ISBN 0-691-02981-4, paper
Author: Curtis T. McMullen
Title: Renormalization and 3-manifolds which fiber over the circle
Additional book information: Princeton University Press, 1996, vii + 253 pp.; ISBN 0-691-01154-0, cloth; ISBN 0-691-01153-2, paper
- [DH1] Adrien Douady and John Hamal Hubbard, On the dynamics of polynomial-like mappings, Ann. Sci. École Norm. Sup. (4) 18 (1985), no. 2, 287–343. MR 816367
- [DH2] Adrien Douady and John H. Hubbard, A proof of Thurston’s topological characterization of rational functions, Acta Math. 171 (1993), no. 2, 263–297. MR 1251582, https://doi.org/10.1007/BF02392534
- [F] Mitchell J. Feigenbaum, Quantitative universality for a class of nonlinear transformations, J. Statist. Phys. 19 (1978), no. 1, 25–52. MR 501179, https://doi.org/10.1007/BF01020332
- [L1] Mikhail Lyubich, Dynamics of quadratic polynomials. I, II, Acta Math. 178 (1997), no. 2, 185–247, 247–297. MR 1459261, https://doi.org/10.1007/BF02392694
- [L2] M. Lyubich. Feigenbaum-Coullet-Tresser Universality and Milnor's Hairiness Conjecture. To appear in Ann. Math.
- [MS] Welington de Melo and Sebastian van Strien, One-dimensional dynamics, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 25, Springer-Verlag, Berlin, 1993. MR 1239171
- [M] John Milnor, Self-similarity and hairiness in the Mandelbrot set, Computers in geometry and topology (Chicago, IL, 1986) Lecture Notes in Pure and Appl. Math., vol. 114, Dekker, New York, 1989, pp. 211–257. MR 988699
- [MT] John Milnor and William Thurston, On iterated maps of the interval, Dynamical systems (College Park, MD, 1986–87) Lecture Notes in Math., vol. 1342, Springer, Berlin, 1988, pp. 465–563. MR 970571, https://doi.org/10.1007/BFb0082847
- [S1] Dennis Sullivan, Quasiconformal homeomorphisms in dynamics, topology, and geometry, Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Berkeley, Calif., 1986) Amer. Math. Soc., Providence, RI, 1987, pp. 1216–1228. MR 934326
- [S2] Dennis Sullivan, Bounds, quadratic differentials, and renormalization conjectures, American Mathematical Society centennial publications, Vol. II (Providence, RI, 1988) Amer. Math. Soc., Providence, RI, 1992, pp. 417–466. MR 1184622
- [TC] Charles Tresser and Pierre Coullet, Itérations d’endomorphismes et groupe de renormalisation, C. R. Acad. Sci. Paris Sér. A-B 287 (1978), no. 7, A577–A580 (French, with English summary). MR 512110
Review Information:
Reviewer: Mikhail Lyubich
Email: mlyubich@math.sunysb.edu
Journal: Bull. Amer. Math. Soc. 36 (1999), 103-107
MSC (1991): Primary 58F23
DOI: https://doi.org/10.1090/S0273-0979-99-00770-3
Review copyright: © Copyright 1999 American Mathematical Society