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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.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Book Review

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

MathSciNet review: 2869012
Full text of review: PDF   This review is available free of charge.
Book Information:

Authors: Feliks Przytycki and Mariusz Urbański
Title: Conformal fractals: ergodic theory methods
Additional book information: London Mathematical Society Lecture Note Series, 371, Cambridge University Press, Cambridge, 2010, x+354 pp., ISBN 978-0-521-43800-1

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

  • Alan F. Beardon, Iteration of rational functions, Graduate Texts in Mathematics, vol. 132, Springer-Verlag, New York, 1991. Complex analytic dynamical systems. MR 1128089, DOI 10.1007/978-1-4612-4422-6
  • Lennart Carleson and Theodore W. Gamelin, Complex dynamics, Universitext: Tracts in Mathematics, Springer-Verlag, New York, 1993. MR 1230383, DOI 10.1007/978-1-4612-4364-9
  • A. Connes, Classification of injective factors. Cases $II_{1},$ $II_{\infty },$ $III_{\lambda },$ $\lambda \not =1$, Ann. of Math. (2) 104 (1976), no. 1, 73–115. MR 454659, DOI 10.2307/1971057
  • Alain Connes and Masamichi Takesaki, The flow of weights on factors of type $\textrm {III}$, Tohoku Math. J. (2) 29 (1977), no. 4, 473–575. MR 480760, DOI 10.2748/tmj/1178240493
  • M. Denker and M. Urbański, Hausdorff measures on Julia sets of subexpanding rational maps, Israel J. Math. 76 (1991), no. 1-2, 193–214. MR 1177340, DOI 10.1007/BF02782852
  • Alexandre Freire, Artur Lopes, and Ricardo Mañé, An invariant measure for rational maps, Bol. Soc. Brasil. Mat. 14 (1983), no. 1, 45–62. MR 736568, DOI 10.1007/BF02584744
  • Harry Furstenberg, Ergodic behavior of diagonal measures and a theorem of Szemerédi on arithmetic progressions, J. Analyse Math. 31 (1977), 204–256. MR 498471, DOI 10.1007/BF02813304
  • H. Furstenberg, Recurrence in ergodic theory and combinatorial number theory, Princeton University Press, Princeton, N.J., 1981. M. B. Porter Lectures. MR 603625
  • Jane Hawkins, Lebesgue ergodic rational maps in parameter space, Internat. J. Bifur. Chaos Appl. Sci. Engrg. 13 (2003), no. 6, 1423–1447. MR 1992056, DOI 10.1142/S021812740300731X
  • Gerhard Keller, Equilibrium states in ergodic theory, London Mathematical Society Student Texts, vol. 42, Cambridge University Press, Cambridge, 1998. MR 1618769, DOI 10.1017/CBO9781107359987
  • Wolfgang Krieger, On ergodic flows and the isomorphism of factors, Math. Ann. 223 (1976), no. 1, 19–70. MR 415341, DOI 10.1007/BF01360278
  • M. Ju. Ljubich, Entropy properties of rational endomorphisms of the Riemann sphere, Ergodic Theory Dynam. Systems 3 (1983), no. 3, 351–385. MR 741393, DOI 10.1017/S0143385700002030
  • Ricardo Mañé, On the uniqueness of the maximizing measure for rational maps, Bol. Soc. Brasil. Mat. 14 (1983), no. 1, 27–43. MR 736567, DOI 10.1007/BF02584743
  • John Milnor, Dynamics in one complex variable, 3rd ed., Annals of Mathematics Studies, vol. 160, Princeton University Press, Princeton, NJ, 2006. MR 2193309
  • V. A. Rohlin, On the fundamental ideas of measure theory, Amer. Math. Soc. Translation 1952 (1952), no. 71, 55. MR 0047744
  • C. E. Shannon, A mathematical theory of communication, Bell System Tech. J. 27 (1948), 379–423, 623–656. MR 26286, DOI 10.1002/j.1538-7305.1948.tb01338.x
  • 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
  • Terence Tao, Norm convergence of multiple ergodic averages for commuting transformations, Ergodic Theory Dynam. Systems 28 (2008), no. 2, 657–688. MR 2408398, DOI 10.1017/S0143385708000011
  • Mariusz Urbański, Measures and dimensions in conformal dynamics, Bull. Amer. Math. Soc. (N.S.) 40 (2003), no. 3, 281–321. MR 1978566, DOI 10.1090/S0273-0979-03-00985-6
  • Anna Zdunik, Parabolic orbifolds and the dimension of the maximal measure for rational maps, Invent. Math. 99 (1990), no. 3, 627–649. MR 1032883, DOI 10.1007/BF01234434
  • M. Zinmeister, Thermodynamic Formalism and Holomorphic Dynamical Systems, SMF/AMS Texts and Mono., Vol. 2 (2000), AMS; in French (1996), SMF.

  • Review Information:

    Reviewer: Jane Hawkins
    Affiliation: University of North Carolina, Chapel Hill, North Carolina
    Journal: Bull. Amer. Math. Soc. 49 (2012), 181-186
    Published electronically: May 16, 2011
    Review copyright: © Copyright 2011 American Mathematical Society