0
votes
0answers
92 views

doubt in a book proof from 'The Geometry of Fractal Sets'

I am reading the proof of existence of positive finite $H^s$-measure (Theorem 5.4) on page 67-68 of The Geometry of Fractal Sets.I am not quite convinced that $E_k$ are closed set by the construction ...
5
votes
1answer
293 views

Hausdorff Dimension of Arbitrary Julia Set

I am looking to find an exact solution to the Hausdorff dimension of a Julia set $J(f)$ for a polynomial $f: z \mapsto z^2 +c$ given an arbitrary $c$. I know this question is known for a number of ...
5
votes
0answers
77 views

How difficult is it to impose a differential structure on a fractal?

Assuming we have a 4-dimensional smooth manifold $M$ embedded in $\mathbb{R}^{m}$ that is difficult to understand its differential structure. For convenience's sake we can assume it is compact, simply ...