4 problems

Let $S^3$ denote the three-dimensional sphere. A diffeomorphism is robustly transitive if its transitivity persists under sufficiently small perturbations in the $C^1$ topology. Sp…

Let $X$ be a robustly transitive contact flow, meaning a contact flow that remains topologically transitive under the relevant perturbations within the class of contact flows. Cont…

Let $g$ be a Riemannian metric whose geodesic flow is robustly transitive, meaning that $g$ admits a $C^2$-neighbourhood such that every metric in that neighbourhood has topologica…

Let $M$ and $N$ be closed manifolds of arbitrary finite dimension. Suppose that $M$ supports an expanding map $F$. Product-map conjecture. The product $M\times N$ supports a $C^1$…