Significant Curves of the Mandelbrot Set

  • Dalibor Martisek Institute of Mathematics, Brno University of Technology
Keywords: Mandelbrot Set, Main Hyperbolic Component, Internal Bound, External Bound, Resultant of Polynomials

Abstract

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.

References

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Goldberg, L., and Tresser, C. Rotation orbits and the farey tree. Ergodic Theory and Dynamical Systems 16, 5 (1996), 1011–1029.

Published
2021-12-21
How to Cite
[1]
Martisek, D. 2021. Significant Curves of the Mandelbrot Set. MENDEL. 27, 2 (Dec. 2021), 30-35. DOI:https://doi.org/10.13164/mendel.2021.2.030.
Section
Articles