Significant Curves of the Mandelbrot Set
The paper provides a description of some interesant curves contained in the Mandelbrot set. These curves are the boundaries of the areas called „bulbs“ which are described approximately only in present. In this paper, some of them are described analyticaly – curves of so called first period, the boundary of the main hyperbolic component, internal and external bounds and also some curves of the second period.
Devaney, R. The fractal geometry of the mandelbrot set ii: How to add and how to count. Fractals 03, 04 (1995), 629–650.
Devaney, R. Unveiling the mandelbrot set. Plus Magazine 40 (2006).
Douady, A., and Hubbard, J. H. It´eration des polynˆomes quadratiques complexes (iteration of complex quadratic polynomials). C. R. Acad. Sci., Paris, S´er. I 294 (1982), 123–125.
Fowler, A., and McGuinness, M. The size of mandelbrot bulbs. Chaos, Solitons Fractals: X 3 (2019), 100019.
Goldberg, L., and Tresser, C. Rotation orbits and the farey tree. Ergodic Theory and Dynamical Systems 16, 5 (1996), 1011–1029.
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