An abstract KAM theorem is developed for infinitely many weakly interacting particles with decaying masses, enabling construction of full-dimensional invariant tori in infinite-dimensional systems with long-range interactions.
Duke Math
2 Pith papers cite this work. Polarity classification is still indexing.
2
Pith papers citing it
fields
math.DS 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
A weighted Sobolev space on the torus has sharp regularity that lets KAM theory apply to perturbations with classical differentiability only up to floor(n/2) while higher weak derivatives remain unbounded.
citing papers explorer
-
Kolmogorov invariant torus theorem for weakly interacting particles I: Full dimensional tori
An abstract KAM theorem is developed for infinitely many weakly interacting particles with decaying masses, enabling construction of full-dimensional invariant tori in infinite-dimensional systems with long-range interactions.
-
Sharp regularity of a weighted Sobolev space over $ \mathbb{T}^n $ and its relation to finitely differentiable KAM theory
A weighted Sobolev space on the torus has sharp regularity that lets KAM theory apply to perturbations with classical differentiability only up to floor(n/2) while higher weak derivatives remain unbounded.