A study of dynamics of the tricomplex polynomial $$\eta ^p+c$$ηp+c

@article{Paris2014ASO,
  title={A study of dynamics of the tricomplex polynomial \$\$\eta ^p+c\$\$ηp+c},
  author={Pierre-Olivier Paris{\'e} and D. Rochon},
  journal={Nonlinear Dynamics},
  year={2014},
  volume={82},
  pages={157-171}
}
In this article, we give the exact interval of the cross section of the so-called Mandelbric set generated by the polynomial $$z^3+c$$z3+c where $$z$$z and $$c$$c are complex numbers. Following that result, we show that the Mandelbric defined on the hyperbolic numbers $$\mathbb {D}$$D is a square with its center at the origin. Moreover, we define the Multibrot sets generated by a polynomial of the form $$Q_{p,c}(\eta )=\eta ^p+c$$Qp,c(η)=ηp+c ($$p \in \mathbb {N}$$p∈N and $$p \ge 2$$p≥2) for… Expand
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