Combining rational maps and controlling obstructions

Ergodic Theory and Dynamical Systems

Volumn 18, Issue 1, 1998, Pages 221-245

  Pilgrim, Kevin M ^a   Lei, Tan ^b  

^a White Hall ^*  (United States)

^b UNIVERSITY OF WARWICK   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032342934     PISSN: 01433857     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0143385798100329     Document Type: Article

References (20)

1. D. Ahmadi. Dynamics of certain rational maps of degree two. PhD Thesis, University of Liverpool, 1991.
2. B. Branner and A. Douady. Surgery on complex polynomials. Holomorphic Dynamics: Proceedings, Mexico (Lecture Notes in Mathematics 1345). Springer, 1986.
3. A. Douady and J. Hubbard. Etude Dynamique des Polynomes Complexes, I, II. Publications Mathematique Orsay (1984/5).
4. A. Douady and J. Hubbard. A proof of Thurston's topological characterization of rational functions. Acta. Math. 171 (1993), 263-297.
5. P. Doyle and C. McMullen. Solving the quintic by iteration. Acta Math. 163 (1989), 151-180.
6. D. B. A. Epstein. Curves on 2-manifolds and isotopy. Acta Math. 115 (1966), 83-107.
7. F. R. Gantmacher. Theory of Matrices. Chelsea, 1959.
8. J. Head. The combinatorics of Newton's method for cubic polynomials. PhD Thesis, Cornell University, 1992.
9. J. Luo. Combinatorics and holomorphic dynamics: captures, matings, Newton's method. PhD Thesis, Cornell University, 1995.
10. C. McMullen. Families of rational maps and iterative root-finding algorithms. Annals of Math. 125 (1987), 467-493.
11. J. Milnor. Dynamics in one complex variable: introductory lectures. Preprint, SUNY Stonybrook Institute for Mathematical Sciences (1990/5).
12. K. M. Pilgrim. Rational maps whose Fatou components are Jordan domains. Ergod. Th. & Dynam. Sys. 16 (1996), 1323-1343.
13. K. M. Pilgrim. Cylinders for iterated rational maps. PhD Thesis, University of California at Berkeley, May, 1994.
14. A. Poirier. On post-critically finite polynomials part two: Hubbard trees. Preprint, SUNY Stony Brook Institute for Mathematical Sciences (1993/7).
15. M. Rees. A partial description of the parameter space of rational maps of degree two: part I. Acta Math. 168 (1992), 11-87.
16. M. Shishikura. On the quasiconformal surgery of rational functions. Ann. Sci. Éc. Norm. Sup. 20 (1987).
17. M. Shishikura and Tan Lei. A Family of cubic rational maps and matings of cubic polynomials. Preprint, Max-Planck Institut für Mathematik (1988).
18. Tan Lei. Matings of quadratic polynomials. Ergod. Th. & Dynam. Sys. (1992), 589-620.
19. Tan Lei. Branched coverings and cubic Newton maps. Fundamenta Mathematicae. To appear.
20. B. Wittner. On the bifurcation loci of rational maps of degree two. PhD Thesis, Cornell University, 1986.