8 problems

Repelling 45-lines conjecture. On the $45$-lines $h_{19}$ is repelling and, hence, $\{X=0\}$ resides in the Julia set $J_{h_{19}}$.

Attracting-orbit conjecture. The only attracting periodic points for $h_{19}$ are the elements of ${\mathcal{O}_{72}}$. Moreover, the union of the basins of attraction for…

Let $f_{6}$ be the map under discussion on ${\mathbf{CP}^{3}}$, and let the $5$-point orbit denote the orbit of the $5$-points. The basins of an attracting orbit are the sets of po…

Let $h_{11}$ be the map under discussion, and let ${\mathcal R}$ be the ${\mathcal S}_{5}$-symmetric real projective subspace ${\mathbf{RP}^{3}}$ preserved by $h_{11}$. The Julia s…

Let $h_{11}$ be the map under discussion on ${\mathbf{CP}^{3}}$, and let the $20$-point orbit denote the orbit of the octahedral $20$-points. A basin is the set of points whose ite…

Let $\mathcal A$ be a linear cocycle over a base transformation $T$. Consider the following properties: (a) $\mathcal A$ has dominated splittings of all indices $0<i<n$; (b) the pr…

Let $f$ be a holomorphic self-map of degree $d$ on $\mathbb{P}^k$, with Green current $T$. Define … so that…

Let $f$ be an endomorphism of algebraic degree $d\geq 2$ of $\mathbb{P}^k$, and let $\mu$ be its equilibrium measure. Let $\chi_1,\ldots,\chi_k$ be the Lyapounov exponents of $\mu$…