Geometry and Dynamics of Quadratic Rational Maps

REFERENCES

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