5 problems

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 $T\colon X\to X$ be a basic hyperbolic homeomorphism, for example a full shift, and let $V$ be a smooth vector bundle on $X$. For $r\geq 0$, let $LC^r_{V,T}$ denote the space o…

Let $\hat{A}_k$ and $\hat{A}$ be continuous linear cocycles over the same hyperbolic system. Suppose that each cocycle is equipped with a uniform unstable holonomy $H^{u,k}$ and…

Self-affine full-dimension conjecture. Then $T_1,\ldots,T_N$ are similitudes with respect to some inner product on $\mathbb{R}^d$.

Let $T\colon W\rightarrow W$ have the closing by periodic orbits property, and let $\boldsymbol{C}\in\operatorname{C}(W,\mathbb{R}^{d\times d})$ be a continuous matrix-valued funct…