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<p>This paper presents the conditions that preserve the partial frequencies and partial frequency ratios for multiscale Hamiltonian systems. These conditions involve both ordered and disordered relationships among the multiscales, leading to significant challenges in the KAM steps. At the end of the paper, we provide an application in the context of the spatially restricted three-body problem involving comets.</p>

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Partial Frequency and Frequency Ratio in Multiscale KAM Formulism

  • 期刊论文

  • 发表日期：

    2025年3月18日

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  • Weichao Qian,
  • Xue Yang,
  • Yong Li

摘要

This paper presents the conditions that preserve the partial frequencies and partial frequency ratios for multiscale Hamiltonian systems. These conditions involve both ordered and disordered relationships among the multiscales, leading to significant challenges in the KAM steps. At the end of the paper, we provide an application in the context of the spatially restricted three-body problem involving comets.