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Bulletin of the American Mathematical Society

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Frontiers in complex dynamics


Author: Curtis T. McMullen
Journal: Bull. Amer. Math. Soc. 31 (1994), 155-172
MSC: Primary 58F23; Secondary 30D05
DOI: https://doi.org/10.1090/S0273-0979-1994-00519-1
MathSciNet review: 1260523
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  • [Bea] A. Beardon, Iteration of rational functions, Springer-Verlag, New York, 1991. MR 1128089 (92j:30026)
  • [BR] L. Bers and H. L. Royden, Holomorphic families of injections, Acta Math. 157 (1986), 259-286. MR 857675 (88i:30034)
  • [Bl] P. Blanchard, Complex analytic dynamics on the Riemann sphere, Bull. Amer. Math. Soc. (N.S.) 11 (1984), 85-141. MR 741725 (85h:58001)
  • [BH1] B. Branner and J. H. Hubbard, The iteration of cubic polynomials, Part I: The global topology of parameter space, Acta Math. 160 (1988), 143-206. MR 945011 (90d:30073)
  • [BH2] -, The iteration of cubic polynomials, Part II: Patterns and parapatterns, Acta Math. 169 (1992), 229-325. MR 1194004 (94d:30044)
  • [CG] L. Carleson and T. Gamelin, Complex dynamics, Springer-Verlag, New York, 1993. MR 1230383 (94h:30033)
  • [CS] S. S. Chern and S. Smale, eds., Global analysis, Amer. Math. Soc., Providence, RI, 1970. MR 0263081 (41:7686)
  • [Cvi] P. Cvitanović, Universality in chaos, Adam Hilger Ltd., New York, 1984. MR 766402 (86f:58044)
  • [Dou1] A. Douady, Systèmes dynamiques holomorphes, Astérisque 105-106 (1983), 39-64. MR 728980 (85h:58090)
  • [Dou2] -, Descriptions of compact sets in C, Topological Methods in Modern Mathematics (L. R. Goldberg and A. V. Phillips, eds.), Publish or Perish, Cambridge, MA, 1993, pp. 429-465. MR 1215973 (94g:58185)
  • [DH] A. Douady and J. Hubbard, On the dynamics of polynomial-like mappings, Ann. Sci. École. Norm. Sup. (4) 18 (1985), 287-344. MR 816367 (87f:58083)
  • [DMc] P. Doyle and C. McMullen, Solving the quintic by iteration, Acta Math. 163 (1989), 151-180. MR 1032073 (91d:12004)
  • [EL] E. L. Eremenko and M. Lyubich, The dynamics of analytic transformations, Leningrad Math. J. 1 (1990), 563-634. MR 1015124 (91b:58109)
  • [Fatou] P. Fatou, Sur les équations fonctionnelles (Deuxiéme mémoire), Bull. Sci. Math. France 48 (1920), 33-94. MR 1504792
  • [Hub] J. H. Hubbard, Local connectivity of Julia sets and bifurcation loci: Three theorems of J.-C. Yoccoz, Topological Methods in Modern Mathematics (L. R. Goldberg and A. V. Phillips, eds.), Publish or Perish, Cambridge, MA, 1993, pp. 467-511. MR 1215974 (94c:58172)
  • [Jak] M. V. Jakobson, Absolutely continuous invariant measures for one-parameter families of one-dimensional maps, Comm. Math. Phys. 81 (1981), 39-88. MR 630331 (83j:58070)
  • [Lat] S. Lattès, Sur l'iteration des substitutions rationelles et les fonctions de Poincaré, C. R. Acad. Sci. Paris Sér. I Math. 166 (1918), 26-28.
  • [Lyu1] M. Lyubich, An analysis of the stability of the dynamics of rational functions, Selecta Math. Sov. 9 (1990), 69-90.
  • [Lyu2] -, Geometry of quadratic polynomials: Moduli, rigidity, and local connectivity, Stony Brook IMS Preprint 1993/9.
  • [Mane] R. Mañé, A proof of the $ {C^1}$ stability conjecture, Publ. Math. Inst. Hautes Études Sci. 66 (1988), 160-210.
  • [MSS] R. Mañé, P. Sad, and D. Sullivan, On the dynamics of rational maps, Ann. Sci. École. Norm. Sup. (4) 16 (1983), 193-217. MR 732343 (85j:58089)
  • [Mc] C. McMullen, Complex dynamics and renormalization, Princeton Univ. Press, Princeton, NJ (to appear). MR 1312365 (96b:58097)
  • [McS] C. McMullen and D. Sullivan, Quasiconformal homeomorphisms and dynamics III: The Teichmüller space of a holomorphic dynamical system, preprint. MR 1620850 (99e:58145)
  • [Mil1] J. Milnor, Self-similarity and hairiness in the Mandelbrot set, Computers in Geometry and Topology (M. C. Tangora, ed.), Lecture Notes in Pure and Appl. Math., Dekker, New York, 1989. MR 988699 (90c:58086)
  • [Mil2] -, Dynamics in one complex variable: Introductory lectures, Stony Brook IMS Preprint 1990/5. MR 1721240 (2002i:37057)
  • [Mil3] -, Local connectivity of Julia sets: Expository lectures, Stony Brook IMS Preprint 1992/11.
  • [Mil4] -, Remarks on iterated cubic maps, Experimental Math. 1 (1992), 5-24. MR 1181083 (94c:58096)
  • [Mil5] -, Geometry and dynamics of quadratic rational maps, Experimental Math. 2 (1993), 37-83. MR 1246482 (96b:58094)
  • [Rees1] M. Rees, Positive measure sets of ergodic rational maps, Ann. Sci. École. Norm. Sup. (4) 19 (1986), 383-407. MR 870689 (88g:58100)
  • [Rees2] -, Components of degree 2 hyperbolic rational maps, Invent. Math. 100 (1990), 357-382. MR 1047139 (91b:58187)
  • [Rees3] -, A partial description of parameter space of rational maps of degree two: Part I, Acta Math. 168 (1992), 11-87. MR 1149864 (93f:58205)
  • [Shi] M. Shishikura, The Hausdorff dimension of the boundary of the Mandelbrot set and Julia sets, Ann. of Math. (to appear). MR 1626737 (2000f:37056)
  • [Smale] S. Smale, Structurally stable systems are not dense, Amer. J. Math. 88 (1966), 491-496. MR 0196725 (33:4911)
  • [Sul1] D. Sullivan, On the ergodic theory at infinity of an arbitrary discrete group of hyperbolic motions, Riemann Surfaces and Related Topics: Proceedings of the 1978 Stony Brook Conference, Ann. of Math. Stud., vol. 97, Princeton Univ. Press, Princeton, NJ, 1981. MR 624833 (83f:58052)
  • [Sul2] -, Conformal dynamical systems, Geometric Dynamics, Lecture Notes in Math., vol. 1007, Springer-Verlag, New York, 1983, pp. 725-752. MR 730296 (85m:58112)
  • [Sul3] -, Bounds, quadratic differentials and renormalization conjectures, Mathematics into the Twenty-first Century: 1988 Centennial Symposium, August 8-12 (F. Browder, ed.), Amer. Math. Soc., Providence, RI, 1992. MR 1184622 (93k:58194)
  • [ST] D. Sullivan and W. P. Thurston, Extending holomorphic motions, Acta Math. 157 (1986), 243-258. MR 857674 (88i:30033)
  • [Sw] G. Światek, Hyperbolicity is dense in the real quadratic family, Stony Brook IMS Preprint 1992/10.
  • [Yoc1] J.-C. Yoccoz, Polynômes quadratiques et attracteur de Hénon, Astérisque 201-203 (1991), 143-165. MR 1157841 (93j:58082)
  • [Yoc2] -, Sur la connexité locale des ensembles de Julia et du lieu de connexité des polynômes, in preparation.

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DOI: https://doi.org/10.1090/S0273-0979-1994-00519-1
Article copyright: © Copyright 1994 American Mathematical Society

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