Non-autonomous KAM theory for lower dimensional invariant tori (II): Normally parabolic case

Donato Scarcella; Frank Trujillo

Non-autonomous KAM theory for lower dimensional invariant tori (II): Normally parabolic case

Dynamical Systems 2026-07-30 v1

Authors: Donato Scarcella , Frank Trujillo

Abstract

Dynamical systems subject to non-autonomous perturbations decaying in time arise naturally in many physical contexts, including laser-molecule interactions, epidemiological models, nonlinear oscillatory systems, and celestial mechanics. In this paper, we consider time-dependent perturbations decaying polynomially fast in time of Hamiltonian systems having a lower-dimensional isotropic normally parabolic invariant torus supporting quasiperiodic solutions. We prove the existence of invariant manifolds in the extended phase space, and determine the asymptotic behavior of the associated transverse dynamics. The above results are obtained for H\"older, smooth, and analytic Hamiltonian systems.

Keywords

KAM theory invariant tori normally parabolic non-autonomous perturbations Hamiltonian systems

Cite

@article{arxiv.2607.28472,
  title  = {Non-autonomous KAM theory for lower dimensional invariant tori (II): Normally parabolic case},
  author = {Donato Scarcella and Frank Trujillo},
  journal= {arXiv preprint arXiv:2607.28472},
  year   = {2026}
}