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Dimensions of Mandelbrot Set Boundary and of Julia Sets

In: Quasiconformal Mappings in the Plane and Complex Dynamics

Author

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  • Luis T. Magalhães

    (University of Lisbon, Instituto Superior Técnico)

Abstract

Écalle cylinders theory for analysis of the orbits in a neighborhood of a parabolic fixed point and bifurcations at such a point, initiated in 1984–1985 by Douady and Hubbard, continued in 1989 by Lavaurs and in 1998 by Shishikura. Proofs that the boundary of the Mandelbrot set has Hausdorff dimension 2, as well as generically Julia set of quadratic polynomials for parameter in the Mandelbrot set boundary, with holomorphic motions, Écalle cylinders and structural stability and bifurcation, as by Shishikura in 1998.

Suggested Citation

  • Luis T. Magalhães, 2025. "Dimensions of Mandelbrot Set Boundary and of Julia Sets," Springer Books, in: Quasiconformal Mappings in the Plane and Complex Dynamics, chapter 0, pages 211-249, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-80115-0_7
    DOI: 10.1007/978-3-031-80115-0_7
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