10 problems

No-wandering-domains conjecture. Such a rational map has no wandering domains in $\mathbb{P}^1_{\mathbb{C}_p}$.

Infinite $B_0$ conjecture. If $f$ is a transcendental entire function and $F(f)\not=\emptyset$, then

Uniform boundedness conjecture. If $f(z)\in\Delta$ and $F(f)\not=\emptyset$, then $F(f)$ is uniformly bounded.

Conjecture de pré-périodicité des composantes. Toutes les composantes de l'ensemble de Fatou sont pré-périodiques.

Fatou-set conjecture. For $n\geq 5$, $F_g$ consists of the basins of attraction of the $p_m$-points.

Let $f:\mathbb{C}\to\mathbb{C}$ be a polynomial, and let a Fatou component mean a connected component of the Fatou set of $f$. For $\epsilon>0$, measure diameters in the usual Eucl…

Let … with $\lambda\in\mathbb{C}^*$ and $a\in\mathbb{C}$. Suppose that $f_{\lambda,a}$ is post-critically bounded, meaning that the forward orbits of its critical values are bounde…

Let $f(z)=\sin z$ be the sine function, and consider a vertical strip of width $2\pi$ in the complex plane. Milnor's conjecture. The area of the Fatou set $F(f)$ within such a vert…

Let $f$ be an endomorphism of the $k$-analytic projective space, and let $F_{\mathrm{norm}}(f)$ and $F_{\mathrm{harm}}(f)$ denote its normal and harmonic Fatou sets, respectively.…

Let $M$ be the class of transcendental meromorphic functions $f\colon\mathbb{C}\to\mathbb{C}\cup\{\infty\}$ with at least two poles or one pole that is not an omitted value, and le…