11 problems

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…

Let the … curve be the locus of period-doubling bifurcations, and let … and … denote the homoclinic bifurcation curves associated with the discrete … bifurcation. Termination conje…

Let the spatial restricted four-body problem have Jacobi integral $J=2.55$, masses $m_1=0.4$, $m_2=0.35$, and $m_3=0.25$, and consider the vertical Lyapunov families associated wit…

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

Consider a Hamiltonian system of two degrees of freedom with Moser's normal form near a hyperbolic invariant point. The stable and unstable branches are represented in normal-form…

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 $\phi_\lambda$ 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 $\phi_\lambda$ be the billiard map, let $\Omega_\lambda$ be its nonwandering set, let $P$ be the parabolic attractor, and let $q_n$ be the periodic points introduced in the pap…

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…