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<p>For smooth nearly integrable Hamiltonian systems, KAM theory preserves a large measure set of invariant tori. When the degrees of freedom are greater than 2, the complement of all these tori forms a topologically connected set, enabling the existence of long-range wandering trajectories. In this paper, we propose a constructive method to show that any KAM torus could be the asymptotic limit set of such wandering trajectories. Our result reveals dynamical behaviors more intricate than those in Arnold diffusion.</p>

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Asymptotic trajectories of the KAM torus: A constructive proof

  • 期刊论文

  • 发表日期：

    2025年10月29日

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  • Chong-Qing Cheng,
  • Jianlu Zhang

摘要

For smooth nearly integrable Hamiltonian systems, KAM theory preserves a large measure set of invariant tori. When the degrees of freedom are greater than 2, the complement of all these tori forms a topologically connected set, enabling the existence of long-range wandering trajectories. In this paper, we propose a constructive method to show that any KAM torus could be the asymptotic limit set of such wandering trajectories. Our result reveals dynamical behaviors more intricate than those in Arnold diffusion.