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This article introduces two reduction schemes for Hamiltonian systems on an exact symplectic manifold admitting Lie group symmetries. It is demonstrated that these reduction procedures are equivalent, by employing a modified Marsden–Meyer–Weinstein reduction theorem for exact symplectic manifolds and contact manifolds given by energy hypersurfaces. Each approach is illustrated through an example.

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Reduction of Exact Symplectic Manifolds and Energy Hypersurfaces

  • 会议论文

  • 发表日期：

    2026年

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  • J. Lange,
  • B. M. Zawora

摘要

This article introduces two reduction schemes for Hamiltonian systems on an exact symplectic manifold admitting Lie group symmetries. It is demonstrated that these reduction procedures are equivalent, by employing a modified Marsden–Meyer–Weinstein reduction theorem for exact symplectic manifolds and contact manifolds given by energy hypersurfaces. Each approach is illustrated through an example.