9 problems

Let $f$ be a homeomorphism of the two-dimensional torus homotopic to the identity, and let $F$ be a lift of $f$. Its rotation set is … A rotation set is thus a compact convex subse…

Let ${\bf c}=(c_n)_{n\in\mathbb N}$ be a sequence of complex numbers. For every real-coefficient polynomial $P$ of degree at most $d$ and every pair of integers $0\leq l<k$, suppos…

Let $\bbS^2=\bbR^2/\bbZ^2$ be partitioned into four rectangles as the product of partitions $\bbS=\bbS^1=\bbR/\bbZ=\delta^x_1\cup\delta^x_2$ and $\delta^y_1\cup\delta^y_2$. Conside…

Let $n\geq 2$, let ${\mathbb T}^n$ be the $n$-dimensional torus, and let $f$ be a Denjoy-type quasiconformal homeomorphism of ${\mathbb T}^n$. Its wandering domains are the domains…

A homeomorphism $fbrcolon torus^2to torus^2$ is periodic point-free if it has no periodic points, and it is a pseudo-rotation when its rotation set consists of a single vector. Per…

Let $\mathcal{V}$ be the parameter space of finite-type double rotations with a fixed partition, and let the associated map have an attractor. The attractor is semi-continuous with…

Let $\mathcal{V}$ be the parameter space of pairs ${v_0,v_1}$, with a fixed partition, for which the double-rotation map $f_{v_0,v_1}$ on a two-dimensional torus is of finite type.…

Let $\mathbb{T}$ be a two-dimensional torus, let $Rsubseteqmathbb{T}$ be a fixed partition region, and let $v_0,v_1inmathbb{R}^2$. The associated double rotation is the map…

Let ${\mathbb T}^{2n}$ be the standard symplectic torus, and let a symplectomorphism of ${\mathbb T}^{2n}$ have a flux that is “sufficiently irrational” and at least one homologica…