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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

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

  • [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

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
American Mathematical Society