7 problems

A complex quadratic is a polynomial of the form $z\mapsto z^2+c$. A polynomial is non-hyperbolic when it is not hyperbolic, and it is topologically rigid when it is not topological…

Algebraicity conjecture. Anosov diffeomorphisms are always of algebraic nature, up to topological conjugacy.

Let $M$ be a compact topological space, let $\phi\in\operatorname{Hom}(M)$ be a homeomorphism, let $\omega:M\to\mathbb{R}^d$ be continuous, and let…

Boyle–Maass conjecture. Every mixing topological Markov shift having a positively expansive $c$-to-one endomorphism is topologically conjugate to some full $d$-shift with $c$ and…

Let $f,g:\mathbb{R}^n\to\mathbb{R}^n$ be periodic linear maps, meaning that $f^k=\operatorname{id}_{\mathbb{R}^n}$ and $g^\ell=\operatorname{id}_{\mathbb{R}^n}$ for some positive i…

Świątek's conjecture. The $RCE$ condition is topologically invariant for multimodal analytic maps with negative Schwarzian derivative.

Świątek's conjecture. The $RCE$ condition is topologically invariant for multimodal analytic maps with negative Schwarzian derivative: if two such maps are topologically conjugate,…