Advertisement

The Journal of Analysis

, Volume 24, Issue 1, pp 95–101 | Cite as

Cross-sections of multibrot sets

  • Line Baribeau
  • Thomas Ransford
Others

Abstract

We identify the intersection of the multibrot set of \(z^d+c\) with the rays \({\mathbb R}^+\omega \), where \(\omega ^{d-1}=\pm 1\).

Keywords

Mandelbrot set Multibrot set 

Mathematics Subject Classification

37F45 

Notes

Acknowledgements

The first author thanks the organizers of the Conference on Modern Aspects of Complex Geometry, held at the University of Cincinnati in honor of Taft Professor David Minda, for their kind hospitality and financial support. The second author was supported by grants from NSERC and the Canada research chairs program.

References

  1. Lau, E., and D. Schleicher. 1996. Symmetries of fractals revisited. Mathematical Intelligencer 18(1): 45–51.MathSciNetCrossRefzbMATHGoogle Scholar
  2. Parisé, P.O., Ransford, T., and Rochon, D. 2016. Tricomplex dynamical systems generated by polynomials of odd degree (Preprint).Google Scholar
  3. Parisé, P.O., and Rochon, D. 2015a. A study of dynamics of the tricomplex polynomial \(\eta ^p+c\). Nonlinear Dynamics 82(1–2): 157–171.MathSciNetCrossRefzbMATHGoogle Scholar
  4. Parisé, P.O., and Rochon, D. 2015b. Tricomplex dynamical systems generated by polynomials of odd degree (Preprint).Google Scholar
  5. Schleicher, D. 2004. On fibers and local connectivity of Mandelbrot and Multibrot sets. In Fractal geometry and applications: a jubilee of Benoît Mandelbrot. Part 1, Proceedings of Symposia in Pure Mathematics, vol. 72, 477–517. American Mathematical Society, Providence, RI.Google Scholar

Copyright information

© Forum D'Analystes, Chennai 2016

Authors and Affiliations

  1. 1.Département de mathématiques et de statistiqueUniversité LavalQuébecCanada

Personalised recommendations