On rational maps with two critical points

Experimental Mathematics

Volumn 9, Issue 4, 2000, Pages 481-522

  Milnor, John ^a  

^a STONY BROOK UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034348633     PISSN: 10586458     EISSN: 1944950X     Source Type: Journal    
DOI: 10.1080/10586458.2000.10504657     Document Type: Article

References (33)

1. L. V. Ahlfors, Lectures on quasiconformal mappings, Van Nostrand Math. Studies 10, Van Nostrand, Toronto, 1966. Reprinted by Wadsworth and Brooks/Cole, Monterey, CA, 1987.
2. P. Alexandroff and H. Hopf, Topologie I, Grundlehren der mathematischen Wissenschaften 45, Springer, Berlin, 1935. Reprinted by Chelsea, 1972, and by Springer, 1974.
3. d have no Herman rings”, Proc. Amer. Math. Soc. 127: 2 (1999), 633-636.
4. W. Bergweiler, “Iteration of meromorphic functions”, Bull. Amer. Math. Soc. (N.S.) 29: 2 (1993), 151-188.
5. T. Bousch, Sur quelques problemes de la dynamique holomorphique, these, Orsay, 1992.
6. L. Carleson and T. W. Gamelin, Complex dynamics, Springer, New York, 1993.
7. z: dynamics and bifurcations”, Intemat. J. Bifur. Chaos Appl. Sci. Engrg. 1: 2 (1991), 287-308.
8. R. L. Devaney and L. Keen, “Dynamics of maps with constant Schwarzian derivative”, pp. 93-100 in Complex analysis (Joensuu 1987), edited by I. Laine et al., Lecture Notes in Math. 1351, Springer, Berlin, 1988.
9. R. L. Devaney and L. Keen, “Dynamics of tangent”, pp. 105-111 in Dynamical systems (College Park, MD, 1986-87), edited by J. C. Alexander, Lecture Notes in Math. 1342, Springer, Berlin, 1988.
10. R. L. Devaney and L. Keen, “Dynamics of meromorphic maps: maps with polynomial Schwarzian derivative”, Ann. Sci. Ecole Norm. Sup. (4) 22: 1 (1989), 55-79.
11. R. Devaney, L. R. Goldberg, and J. H. Hubbard, “A dynamical approximation to the exponential map by polynomials”, preprint, Berkeley, 1986.
12. A. Douady and J. H. Hubbard, Etude dynamique des polynomes complexes, II, Universite de Paris-Sud, Departement de Mathematique, Orsay, 1985.
13. A. Douady and J. H. Hubbard, “On the dynamics of polynomial-like mappings”, Ann. Sci. Ecole Norm. Sup. (4) 18: 2 (1985), 287-343.
14. L. R. Goldberg and L. Keen, “The mapping class group of a generic quadratic rational map and automorphisms of the 2-shift”, Invent. Math. 101: 2 (1990), 335-372.
15. E. Lau and D. Schleicher, “Internal addresses in the Mandelbrot set and irreducibility of polynomials”, IMS preprint 1994/19, SUNY Stony Brook, 1994.
16. E. Lau and D. Schleicher, “Symmetries of fractals revisited”, Math. Intelligencer 18: 1 (1996), 45-51.
17. Erratum in 18: 2 (1996), p. 53.
18. P. Makienko, “Totally diconnected Julia sets”, preprint 042-95, Math. Sci. Res. Inst., Berkeley, 1995.
19. J. Milnor, “Geometry and dynamics of quadratic rational maps”, Experiment. Math. 2: 1 (1993), 37-83. With an appendix by the author and Lei Tan.
20. J. Milnor, Dynamics in one complex variable: introductory lectures, Vieweg, Braunschweig, 1999. Introductory lectures.
21. J. Milnor, “Periodic orbits, externals rays and the Mandelbrot set: an expository account”, pp. xiii, 277-333 in Geometrie complexe et systemes dynamiques (Orsay, 1995), edited by M. Flexor et al., Asterisque 261, 2000.
22. S. Nakane and D. Schleicher, “Non-local connectivity of the tricorn and multicorns”, pp. 200-203 in Dynamical systems and chaos (Hachioji, 1994), vol. 1, World Scientific, River Edge, NJ, 1995. See also “On multicorns and unicorns: the dynamics of antiholomorphic polynomials”, in preparation.
23. F. Przytycki, “Iterations of rational functions: which hyperbolic components contain polynomials?”, Fund. Math. 149: 2 (1996), 95-118.
24. M. Rees, “Positive measure sets of ergodic rational maps”, Ann. Sci. Ecole Norm. Sup. (4) 19: 3 (1986), 383-407.
25. M. Rees, “Components of degree two hyperbolic rational maps”, Invent. Math. 100: 2 (1990), 357-382.
26. M. Rees, “Views of parameter space: topographer and resident”. In preparation.
27. M. Shishikura, “On the quasiconformal surgery of rational functions”, Ann. Sci. Ecole Norm. Sup. (4) 20: 1 (1987), 1-29.
28. J. H. Silverman, “The space of rational maps on P1”, Duke Math. J. 94: 1 (1998), 41-77.
29. N. Steinmetz, Rational iteration: Complex analytic dynamical systems, de Gruyter Studies in Math. 16, de Gruyter, Berlin, 1993.
30. J. Stimson, Degree two rational maps with a periodic critical point, Thesis, Univ. of Liverpool, 1993.
31. Tan Lei, “Matings of quadratic polynomials”, Ergodic Theory Dynamical Systems 12: 3 (1992), 589-620.
32. Tan Lei, Sur quelques aspects de I’iteration des fractions rationnelles, These d’habilitation, Universite de Lyon, 1997. The author can be reached at tanlei@math.u-cergy.fr.
33. Tan Lei and Y. Yin, “Local connectivity of the Julia set for geometrically finite rational maps”, Sci. China Ser. A 39: 1 (1996), 39-47.