5 problems

Simple-dynamics conjectures. The following properties hold:

Alpha-limit conjecture. There is some non-empty open subset $A\subset f(\mathbb{R}\mathrm{P}^2)$ such that $\alpha_{N_f}(x)$ is equal to the set of non-regular points of the bounda…

Weak plainness conjecture. Then:

Plainness conjecture. Every $p$ satisfying the hypotheses of Barna's theorem is a plain map.

Tan Lei's parameter-space conjecture. The fundamental part of the cubic Newton family is homeomorphic to the quotient of the union of those two subsets by the equivalence relation…