The iteration of cubic polynomials Part I: The global topology of parameter space
نویسندگان
چکیده
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 CHAPTER I. Univalent functions in complex analytic dynamics . . . . . . 147 1. Attraction to infinity . . . . . . . . . . . . . . . . . . . . . . . 147 2. Parametrizing the space of polynomials . . . . . . . . . . . . . 150 3. Compactness of the connectedness locus . . . . . . . . . . . . 153 4. The mapping q~e is close to the identity . . . . . . . . . . . . . 156 5. The high level sets of H are spheres . . . . . . . . . . . . . . . 160 CHAPTER II. Wringing the complex structure . . . . . . . . . . . . . . . 165 6. Beltrami forms invariant under a polynomial . . . . . . . . . . 166 7. Analytic dependence on parameters . . . . . . . . . . . . . . . 169 8. Stretching and wringing the complex structure . . . . . . . . . 171 9. Continuity on the structural stability set . . . . . . . . . . . . . 177 10. Continuity for cubic polynomials . . . . . . . . . . . . . . . . . 179 CHAPTER III. The global topology of parameter space . . . . . . . . . . 183 11. Fibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 12. The structure of the fiber, part 1 . . . . . . . . . . . . . . . . . 185 13. The structure of the fiber, part 2 . . . . . . . . . . . . . . . . . 193 14. The global topology of parameter space . . . . . . . . . . . . . 197 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
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