@DanielFischer hello, I have a function $F:\Bbb{R}^2\to \Bbb{R}^2$ such that $F(x,y)=(x^2+y^2,y^2)$.
I would like to prove that $\Omega=\{p\in \Bbb{R}^2 ; \lim_{k\to\infty}F^k(p)=0\}$ is a domain, where $F^k$ is the $k$-composed map.
For instance I can, only, prove that $p\in \Omega$ if and only if $F(p)$ is as well in $\Omega$. Don't see how can I prove it's open.
I would like to prove that $\Omega=\{p\in \Bbb{R}^2 ; \lim_{k\to\infty}F^k(p)=0\}$ is a domain, where $F^k$ is the $k$-composed map.
For instance I can, only, prove that $p\in \Omega$ if and only if $F(p)$ is as well in $\Omega$. Don't see how can I prove it's open.
