4 problems

Let $h$ be a function depending on $n\geq 6$ degrees of freedom, and let $\sigma_n^r(I)$ denote the bad set of jets of order $r$ at $I$. For $n=2,3,4,5$, three-jet non-degeneracy i…

Let $h$ be a function of $n$ variables, and let $\Sigma_n^r(I)$ denote the algebraic sets associated with the jets of order $r$ at $I$. A function is three-jet non-degenerate when…

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…