6 problems

Let $M$ be a closed Riemannian manifold, and let $f:M\to M$ be a partially hyperbolic diffeomorphism, meaning that $TM$ admits a $Df$-invariant splitting … where $E^s$ is uniformly…

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…