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arXiv · 2607.28452

Non-autonomous KAM theory for lower dimensional invariant tori (I): Normally elliptic and hyperbolic cases

Donato Scarcella·Frank Trujillo
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Abstract

Many physical phenomena are naturally modeled by dynamical systems subject to non-autonomous perturbations that decay in time, including the interaction of a laser pulse with a molecule, epidemiological models, nonlinear oscillatory systems, and celestial mechanics. In the present paper, we consider time-dependent perturbations decaying in time of Hamiltonian systems having a lower-dimensional isotropic normally elliptic (resp. hyperbolic) invariant torus with quasiperiodic solutions. Under suitable rates of decay in time of the perturbation, 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 (I): Normally elliptic and hyperbolic cases. https://arxiv.org/abs/2607.28452

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