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
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
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
- [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
DOI:
https://doi.org/10.1090/S0273-0979-99-00770-3
Review copyright:
© Copyright 1999
American Mathematical Society