4 problems

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 $f\colon\mathbb{T}^2\to\mathbb{T}^2$ be a homeomorphism homotopic to the identity and let $\tilde f\colon\mathbb{R}^2\to\mathbb{R}^2$ be a lift of $f$. Suppose that the rotatio…

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.…