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<p>We explicitly describe the quaternion Heisenberg group in the dimension 7 and we study the local (optimal) control of the compatible control system. We employ the Hamiltonian viewpoint to find sub-Riemannian geodesics of the corresponding sub-Riemannian structure, and we describe the impact of Lie symmetries on their optimality.</p>

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Local control on quaternion Heisenberg group of dimension 7

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月14日

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  • Jan Eisner,
  • Lenka Zalabová

摘要

We explicitly describe the quaternion Heisenberg group in the dimension 7 and we study the local (optimal) control of the compatible control system. We employ the Hamiltonian viewpoint to find sub-Riemannian geodesics of the corresponding sub-Riemannian structure, and we describe the impact of Lie symmetries on their optimality.