4 problems

Let $\mathcal U$ be the neighborhood of the hyperbolic toral automorphism considered in the source. Local counterexample conjecture. For any $f\in\mathcal U$ there exists…

Let $L$ be a hyperbolic automorphism of $\mathbb T^d$, $d\geq 3$, with simple real spectrum and irreducible characteristic polynomial over $\mathbb Z$. Let $\mathcal U$ be the neig…

Let $f$ and $g$ be topologically conjugate $C^r$, $r>1$, Anosov diffeomorphisms of $\mathbb T^3$ with coinciding periodic data, meaning that the differentials of corresponding retu…

Let $\alpha>1$ and $0<\beta<1$, and let $\hat D_{\alpha,\beta}\subset\operatorname{Diff}^1([0,1])$ be the set of diffeomorphisms whose fixed points are precisely $0$ and $1$, with…