7 problems

Let $M$ be a compact surface, let $\operatorname{Diff}_\mu^r(M)$ denote the space of $C^r$ area-preserving diffeomorphisms of $M$, and let $W^s(p)$ and $W^u(p)$ be the stable and u…

A diffeomorphism $f$ is a diffeomorphism of a compact manifold. Palis's conjecture. Any diffeomorphism can be $C^r$ approximated by a Morse–Smale one or by one exhibiting a transve…

Homoclinic-approximation conjecture. If there exist $x$ and $a,b\geq0$ with $a+b>1$ such that

Let $\phi_\lambda$ be the billiard map, let $\Omega_\lambda$ be its nonwandering set, let $P$ be the parabolic attractor, let $p_\lambda$ be the fixed point, and let $p_n$ be the p…

Let $p_n$ be the periodic points of the billiard map, let $C_0$ and $C_1$ denote homoclinic classes, and let $a_n$, $b_n$, and $b_{17}$ be the parameters appearing in the paper. Tw…

Let $q_n$ be the periodic points of the billiard map, let $W^s(q_n)$ and $W^u(q_n)$ denote their stable and unstable manifolds, and let $c_n$ and $\lambda_1$ be the bifurcation par…

Let a vector field be robustly non-hyperbolic if it belongs to the robustly non-hyperbolic class considered in the conjecture, and let $C^r$ denote the relevant differentiability t…