4 problems

Let $M$ be a closed surface and let $\operatorname{Diff}^1(M)$ denote the space of $C^1$ diffeomorphisms of $M$. A diffeomorphism satisfies Axiom A when its nonwandering set is hyp…

Let $M$ be a connected manifold, and let $f\colon M\to M$ be a $C^1$-generic diffeomorphism. Suppose that the non-wandering set of $f$ has non-empty interior. Generic transitivity…

Irregularity conjecture. Generic points of $C^1$-generic diffeomorphisms are irregular$^+$ outside the basins of sinks.

ABD conjecture. There is a residual set $\mathcal{R}\subset\mathcal{D}iff^{1}(M)$ such that if $f\in\mathcal{R}$ and