3 problems

Generic sink-or-source conjecture. For any integer $r\geq 1$, for any diffeomorphism $f$ in a residual subset $\mathcal R\subset\operatorname{Diff}^r(M)$, a homoclinic class…

Generic mechanical non-volume-hyperbolicity conjecture. For any integer $r\geq 1$, there is a residual subset $\mathcal R$ of $C^r$-diffeomorphisms $f$ such that if…

Let $M$ be a compact manifold, and let $\operatorname{Diff}^1(M)$ be the space of $C^1$ diffeomorphisms. A chain-recurrence class is a sink when it is represented by an attracting…