Geometry and dynamics of quadratic rational maps

Experimental Mathematics

Volumn 2, Issue 1, 1993, Pages 37-83

  Milnor, John ^a   Lei, Tan ^b  

^a STONY BROOK UNIVERSITY   (United States)

^b UNIVERSITÉ DE LYON   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84950776875     PISSN: 10586458     EISSN: 1944950X     Source Type: Journal    
DOI: 10.1080/10586458.1993.10504267     Document Type: Article

References (40)

1. B. Bielefeld, "Questions in quasiconformal surgery", pp. 1-6 in Problems in Holomorphic Dynamics (edited by B. Bielefeld and M. Lyubich), SUNY’Stony Brook IMS preprint 1992/7. Also to appear in Linear and Complex Analysis Problem Book (edited by V. P. Havin and N. K. Nikolskii), Springer-Verlag.
2. P. Blanchard, R. Devaney and L. Keen, "The dynamics of complex polynomials and automorphisms of the shift", Invent. Math. 104 (1991), 545-580.
3. B. Branner and J. H. Hubbard, "The iteration of cubic polynomials, II: Patterns and parapattems", Acta Math. 169 (1992) 229r-325.
4. T. Bousch, "Sur quelques problèmes de dynamique holomorphe", Thesis, Univ. Paris-Sud, Orsay, 1992.
5. A. Douady and J. H. Hubbard, "Itérations des polynômes quadratiques complexes", Comptes R. Acad. Sei. Paris 294 (1982), 123-126.
6. A. Douady and J. H. Hubbard, "Etude dynamique des polynômes complexes F, Publ. Math. Orsay (1984), II (1985).
7. A. Douady and J. H. Hubbard, "On the dynamics of polynomial-like mappings", Ann. Sci. Éc. Norm. Sup. (Paris) 18 (1985), 287-343.
8. P. Doyle and C. McMullen, "Solving the quintic by iteration", Acta Math. 163 (1989), 151-180.
9. L. Goldberg and L. Keen, "The mapping class group of a generic quadratic rational map and automorphisms of the 2-shift", Invent. Math. 101 (1990), 335-372.
10. F. v. Haeseler and H.-O. Peitgen, "Newton’s method and complex dynamical systems", Acta Appl. Math. 13 (1988), 3-58.
11. G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Oxford University Press, Oxford, 1979.
12. P. Lavaurs, "Systèmes dynamiques holomorphës: Explosion de points périodiques paraboliaues", Thesis, Univ. Paris-Sud, Orsay, 1989.
13. M. Lyubich, "An analysis of the stability of the dynamics of rational functions", Punk. Anal, i Pril. 42 (1984), 72-91 (in Russian); translated as Selecta Math. Sov. 9 (1990), 69-90.
14. P. Makienko, in preparation.
15. B. Mandelbrot, The Fractal Geometry of Nature, Freeman, New York, 1982.
16. C. McMullen, "Automorphisms of rational maps", pp. 31-60 in Holomorphic Functions and Moduli, vol. 1 (edited by D. Drasin et al.), MSRI Publ. 10, Springer-Verlag, New York, 1988.
17. J. Milnor, "On cubic polynomials with periodic critical point", in preparation.
18. J. Milnor, "On the 3-dimensional Brieskom manifolds M(p, q, r)", pp. 175-225 in Knots, Groups, and 8-Manifolds (edited by L. P. Neuwirth), Annals of Math. Stud. 84, Princeton U. Press, 1975.
19. J. Milnor, Dynamics in One Complex Variable: Introductory Lectures, SUNY Stony Brook IMS preprint 1990/5.
20. J. Milnor, "Remarks on iterated cubic maps", Experimental Math. 1 (1992), 5-24.
21. J. Milnor, "Hyperbolic components in spaces of polynomial maps", SUNY Stony Brook IMS preprint 1992/3.
22. R. Mañé, P. Sad and D. Sullivan, "On the dynamics of rational maps", Ann. Sci. Éc. Norm. Sup. (Paris) 16 (1983), 193-217.
23. C. Petersen, "A remark on Tan Lei’s mating conjecture" (preprint), Århus Universitet, 1993 #2. Included in "Estimating multipliers of repelling periodic orbits in holomorphic dynamics", Thesis, Århus Universitet, 1993.
24. F. Przytycki, "Polynomials in the hyperbolic components", in preparation.
25. F. Przytycki, "Remarks on the simple connectedness of basins of sinks for iteration of rational maps", pp. 229-235 in Dynamical Systems and Ergodic Theory (edited by K. Krzyzewski), Banach Center Pubi. 23, Polish Scientific Publishers, Warsaw, 1989.
26. M. Rees, "Positive measure sets of ergodic rationed maps", Ann. Sci. Éc. Norm. Sup. (Paris) 19 (1986), 383-407.
27. M. Rees, "Components of degree two hyperbolic rational maps", Invent. Math. 100 (1990), 357-382.
28. M. Rees, "Combinatorial models illustrating variation of dynamics in families of rational maps", in Proc. Int. Congr. Math. Kyoto 1990 (edited by I. Satake), Springer-Verlag, Tokyo, 1991.
29. M. Rees, "A partial description of parameter space of rational maps of degree two", I: Acta Math. 168 (1992), 11-87; II: SUNY Stony Brook IMS preprint 1991/4.
30. G. Segal, "The topology of spaces of rational functions", Acta Math. 143 (1979), 39-72.
31. M. Shishikura, "On the quasiconformal surgery of rational functions", Ann. Sci. Éc. Norm. Sup. (Paris) 20 (1987), 1-29.
32. M. Shishikura, "On a theorem of M. Rees for the matings of polynomials" (preprint), IHES, 1990.
33. J. Stimson, "Degree Two Rational Maps with a Periodic Critical Point", Thesis, University of Liverpool, 1993.
34. D. Sullivan, "Quasiconformal homeomorphisms and dynamics, I: Solution of the Fatou-Julia problem on wandering domains", Ann. Math. 122 (1985), 401-418.
35. Tan Lei, "Accouplements des polynômes complexes", Thesis, Univ. Paris-Sud, Orsay, 1987; also "Mating of quadratic polynomials", to appear.
36. W. P. Thurston, Three-Dimensional Geometry and Topology, vol. 2, in preparation.
37. B. L. van der Waerden, Modem Algebra, vol. 1, 7th ed., Springer-Verlag, New York, 1991.
38. G. T. Whybum, "Topological characterization of the Sierpiński curve", Fundamenta Math. 45 (1958), 320-324.
39. B. Wittner, "On the bifurcation loci of rational maps of degree two", Thesis, Cornell University, 1988.
40. Yin Yongcheng, "On the Julia sets of quadratic rational maps", Complex Variables 18 (1992), 141-147.