5 problems

Let ${\cal T}_{\!\!\mathop{\text{\rm \scriptsize ~per}}\nolimits}'$ be the levels of $T_j$ for which the motion of … is periodic with half the period of the motion in the…

Non-integrability conjecture. The system is non-integrable for the case $2\xi=3(1-C)$; in particular, it does not admit an additional real meromorphic first integral functionally i…

Matsumoto's trajectoid return conjecture. Such bodies exist for almost any path, with the body returning to its original orientation after two or more periods.

Higher-dimensional quantization conjecture. Analogous procedures can be applied for $n>6$ to obtain corresponding integrable quantum systems and, for the free quantum rigid body, a…

In the two-dimensional rough-disk model, let $u$ be the measure characterizing the shape of the cavities and let $alpha(lambda, u)$ be the coefficient in the transversal force, wh…