All Questions
4
questions
3
votes
2
answers
253
views
Points attracting to 0 are dense in $\mathbb C$
I know that the following proposition is true, but at the moment I can't see how to prove it.
Define $f(z)=e^z-1$ for all $z\in \mathbb C$. Then $A:=\{z\in \mathbb C:f^n(z)\to 0\}$ is dense in $\...
- 2,993
1
vote
1
answer
441
views
Mandelbrot set and logistic map connection
I'm currently writing an undergraduate thesis on chaos theory with a particular focus on the connection between the Mandelbrot set and the logistic map. I have found scattered posts on this site, ...
3
votes
1
answer
230
views
Contractibility of connected holomorphic dynamics?
Let $f$ be a function, holomorphic in $\mathbb{C}$, and $K(f)$ its non-escaping set :
$$K(f) = \{ z \in \mathbb{C} : f^{(k)}(z) \nrightarrow_{k \to \infty} \infty \} $$
Question : If $K(f)$ is ...
- 25.5k
8
votes
1
answer
1k
views
Beautiful examples of arc-like continua
A continuum is a nonempty compact, connected metric space.
A continuum $X$ is called arc-like if, for every $\varepsilon>0$, there is a continuous and surjective function $f:X\to [0,1]$ such that $...