Year: 2026
Type: preprint
Abstract: We construct high-frequency perturbations of an integrable exact symplectic twist map which preserve an analytic invariant graph with a prescribed rotation number. Their oscillation frequencies may be any positive integers tending to infinity. For every fixed Gevrey parameter $L>0$, the perturbations tend to zero in a Gevrey-$α$ norm and diverge in a Gevrey-$(α-\varepsilon)$ norm. The frequency class strictly contains the $α$-Brjuno--Rüssmann class, and their difference has cardinality \(2^{\aleph_0}\).
Source: arXiv (Cornell University)
Institution: Beijing Institute of Technology
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7201880731