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arXiv · 2607.28472

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

Donato Scarcella·Frank Trujillo
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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.

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Donato Scarcella, Frank Trujillo. 2026-07-30. Non-autonomous KAM theory for lower dimensional invariant tori (II): Normally parabolic case. https://arxiv.org/abs/2607.28472

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