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arXiv · 2505.00088

Nonintegrability of time-periodic perturbations of analytically integrable systems near homo- and heteroclinic orbits

Kazuyuki Yagasaki
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Abstract

We consider time-periodic perturbations of analytically integrable systems in the sense of Bogoyavlenskij and study their \emph{real-meromorphic} nonintegrability, using a generalized version due to Ayoul and Zung of the Morales-Ramis theory. The perturbation terms are assumed to have finite Fourier series in time, and the perturbed systems are rewritten as higher-dimensional autonomous systems having the small parameter as a state variable. We show that if the Melnikov functions are not constant, then the autonomous systems are not \emph{real-meromorphically} integrable near homo- and heteroclinic orbits. We illustrate the theory for rotational motions of a periodically forced rigid body, which provides a mathematical model of a quadrotor helicopter.

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Kazuyuki Yagasaki. 2025-04-30. Nonintegrability of time-periodic perturbations of analytically integrable systems near homo- and heteroclinic orbits. https://arxiv.org/abs/2505.00088

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