6 problems

Nekhoroshev stability conjecture. Nekhoroshev's theorem actually holds on the set $\mathcal{P}^{\bullet}$.

Let $n\geq 3$ and let ${{\bf m}{\alpha}}_1,\ldots,{{\bf m}{\alpha}}_{n-1}$ denote the steepness indices of the Hamiltonian. Let $a$ be the exponent governing the long-time stabilit…

Consider Hamiltonian systems for which the unperturbed Hamiltonian has different steepness properties, meaning distinct forms or degrees of Nekhoroshev steepness. Nekhoroshev's con…

Let $\mathcal{H}_{l}$ be the unperturbed Hamiltonian in the Hamiltonian system considered above. A function is steep if it satisfies Nekhoroshev's steepness condition, which is wea…

Let $H$ be the quasi-periodically time-dependent Hamiltonian … where $(\theta,I)\in\mathbb T^n\times B$, $(\varphi,J)\in\mathbb T^m\times\mathbb R^m$, $\alpha\in\mathbb R^m$ is non…

Effective stability conjecture. An integrable Hamiltonian is effectively stable if and only if it is rationally steep. The paper notes that effective stability implies rational ste…