Combinatorics and Holomorphic Dynamics: Captures, Matings, Newton's MethodCornell University, 1995 - 232 pages |
Common terms and phrases
2-sphere affine conjugate assume attracting fixed point attraction basin b₁ branched cover chapter connected Julia sets corollary critical fixed points critical value critically finite D₁ d₂ definition degenerate Levy cycle degree d polynomial denoted disk component distinct critical fixed Douady external rays external rays landing Fatou components Fatou set Figure fixed critical points formal mating forward orbit Hence homeomorphic homotopic homotopic rel PF Hubbard tree hyperbolic hyperbolic component immediate attraction basin inflection point inflection value internal ray Jordan curve Jordan domain lemma locally connected M₂ Mandelbrot set multi-curve N₁ n₂ Newton's method Note p1 and p2 points of F preimage proposition 5.6 prove Puzzle partitions quadratic polynomials quadratic rational maps rational map ray with angle Remark repelling fixed point result Riemann sphere Riemann-Hurwitz formula subset theorem 3.2 Thurston equivalent Thurston obstruction topological Newton map type d1 y₁ Yoccoz polynomial г₁