7 problems

Pugh–Shub conjecture. Stable ergodicity is $mathcal{C}^r$-dense among partially hyperbolic diffeomorphisms.

Let $M$ be a compact manifold with volume measure $m$, and let $\operatorname{Diff}^{1}_{m}(M)$ be the space of volume-preserving $C^1$-diffeomorphisms of $M$. For…

Let $M$ be a compact manifold, let $m$ denote Lebesgue measure, and let $\operatorname{Diff}^{1}_{m}(M)$ be the space of $C^1$ Lebesgue-measure-preserving diffeomorphisms. An invar…

Let $M^3$ be a three-dimensional manifold, let $m$ denote Lebesgue measure, and let $\operatorname{Diff}^{1}_{m}(M^3)$ be the space of $C^1$ Lebesgue-measure-preserving diffeomorph…

Let $M$ be a compact manifold, let $m$ denote Lebesgue measure, and let $\operatorname{Diff}^{1}_{m}(M)$ be the space of $C^1$ Lebesgue-measure-preserving diffeomorphisms. A diffeo…

Let $M$ be a smooth compact manifold, let $m$ be a smooth volume measure, and let $\operatorname{Diff}^{1}_{m}(M)$ denote the volume-preserving $C^{1}$ diffeomorphisms. Stable ergo…

Let $M$ be the compact connected manifold under consideration, let $r>1$, and let $\operatorname{Diff}^r_m(M)$ denote the space of $C^r$ volume-preserving diffeomorphisms of $M$, e…