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2 votes
1 answer
187 views

How to find the hyperbolic dimension of map $f(z) = z^2$ of $\overline{\mathbb{C}}$ onto itself?

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 ...
Nirmal Rawat's user avatar
5 votes
1 answer
302 views

An entire function all whose forward orbits are bounded

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 $...
Ali Taghavi's user avatar