The multi-scale KAM persistence without a scaling order for Hamiltonian systems

TL;DR

This paper introduces a new, easily verifiable non-degeneracy condition that ensures the persistence of invariant tori in complex multi-scale Hamiltonian systems, with implications for celestial mechanics.

Contribution

It proposes a novel non-degeneracy condition for invariant tori persistence applicable to disordered multi-scale Hamiltonian systems, simplifying analysis in celestial mechanics.

Findings

New non-degeneracy condition for invariant tori

Applicable to disordered multi-scale Hamiltonian systems

Facilitates analysis in celestial mechanics

Abstract

The persistence of invariant tori in multi-scale Hamiltonian systems is intrinsically linked to the stability of the N-body problem. However, the existing non-degeneracy conditions in disordered scenarios have been formulated too generally, making them difficult to apply directly to celestial mechanics. In this work, we present a readily verifiable non-degeneracy condition for the persistence of invariant tori in disordered multi-scale Hamiltonian systems.