Quantitative Destruction of Lagrangian Torus

Lin Wang

Published 2023-12-04Version 1

Let $P_N$ be a trigonometric polynomial of degree $N$ and satisfy $\|P_N\|_{C^r}\leq \epsilon$. If $P_N$ destroys the Lagrangian torus with the rotation vector $\omega$ of an integrable Hamiltonian system, then {what are the relation among $\epsilon$, $N$, $r$ and the arithmetic property of $\omega$}? By addressing this, we provide quantitatively higher dimensional generalizations of the remarkable results on destruction of invariant circles for the area-preserving twist map by Herman [21] in 1983 and Mather [28] in 1988.