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Let $\mathcal{M}$ the Mandelbrot set, $\mathcal{M}=\{c \in \mathbb{C}: \{Q_c^n(0) \}_{n \in \mathbb{N}} \text{ is bounded, where } Q_c(z)=z^2+c \}$ And let the hyperbolic or stable component, $H_n=\{ ...

I am reading the research article "The Hausdorff dimension of the boundary of Mandelbrot set and Julia sets" by Shishikura. In his article, he defined hyperbolic sets and hyperbolic ...

Edit: I revise the question according to the comment of Gabe Conant. What is an example of a non constant entire function $f:\mathbb{C}\to \mathbb{C}$ which satisfy the following?: For every $...