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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.

Full text of review: PDF   This review is available free of charge.
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

References [Enhancements On Off] (What's this?)

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  • 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, DOI 10.1007/BF02392534
  • Mitchell J. Feigenbaum, Quantitative universality for a class of nonlinear transformations, J. Statist. Phys. 19 (1978), no. 1, 25–52. MR 501179, DOI 10.1007/BF01020332
  • Mikhail Lyubich, Dynamics of quadratic polynomials. I, II, Acta Math. 178 (1997), no. 2, 185–247, 247–297. MR 1459261, DOI 10.1007/BF02392694
  • [L2]
    M. Lyubich. Feigenbaum-Coullet-Tresser Universality and Milnor's Hairiness Conjecture. To appear in Ann. Math.
  • 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, DOI 10.1007/978-3-642-78043-1
  • 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
  • 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, DOI 10.1007/BFb0082847
  • 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
  • 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
  • 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
    Journal: Bull. Amer. Math. Soc. 36 (1999), 103-107
    Review copyright: © Copyright 1999 American Mathematical Society