The Mandelbrot set, theme and variations
著者
書誌事項
The Mandelbrot set, theme and variations
（London Mathematical Society lecture note series, 274）
Cambridge University Press, 2000
- : pbk
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注記
Includes bibliographical references
Some contributions in French
内容説明・目次
内容説明
The Mandelbrot set is a fractal shape that classifies the dynamics of quadratic polynomials. It has a remarkably rich geometric and combinatorial structure. This volume provides a systematic exposition of current knowledge about the Mandelbrot set and presents the latest research in complex dynamics. Topics discussed include the universality and the local connectivity of the Mandelbrot set, parabolic bifurcations, critical circle homeomorphisms, absolutely continuous invariant measures and matings of polynomials, along with the geometry, dimension and local connectivity of Julia sets. In addition to presenting new work, this collection documents important results hitherto unpublished or difficult to find in the literature. This book will be of interest to graduate students in mathematics, physics and mathematical biology, as well as researchers in dynamical systems and Kleinian groups.
目次
- Introduction L.Tan
- Preface J. Hubbard
- 1. The Mandelbrot set is universal C. McMullen
- 2. Baby Mandelbrot sets are born in cauliflowers A. Douady, X. Buff, R. Devaney and P. Sentenac
- 3. Modulation dans l'ensemble de Mandelbrot P. Haissinsky
- 4. Local connectivity of Julia sets: expository lectures J. Milnor
- 5. Holomorphic motions and puzzles (following M. Shishikura) P. Roesch
- 6. Local properties of the Mandelbrot set at parabolic points L.Tan
- 7. Convergence of rational rays in parameter spaces C. Petersen and G. Ryd
- 8. Bounded recurrence of critical points and Jakobson's Theorem S. Luzzatto
- 9. The Herman-Swiatek theorems with applications C. Petersen
- 10. Perturbations d'une fonction linearisable H. Jellouli
- 11. Indice holomorphe et multiplicateur H. Jellouli
- 12. An alternative proof of Mane's theorem on non-expanding Julia sets M. Shishikura and L.Tan
- 13. Geometry and dimension of Julia sets Y. -C. Yin
- 14. On a theorem of Mary Rees for the matings of polynomials M. Shishikura
- 15. Le theoreme d'integrabilite des structures presque complexes A. Douady and X. Buff
- 16. Bifurcation of parabolic fixed points M. Shishikura.
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