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<p>We study Hamiltonian systems whose trajectories can go to infinity of the phase space in a finite time. An extension of the phase space and a set of extensions of the Hamiltonian system trajectories to the extended space are defined. Each of these extensions specifies a Hamiltonian flow in the extended space. Using a flow-invariant measure on the extended space, a representation of the Hamiltonian flow by a unitary group is obtained. The ambiguity of the extension is parameterized by a probability space, and an averaged extension is found.</p>

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Dynamics of Nonlinear Wave Systems Admitting Singularity Formation

  • 期刊论文

  • 发表日期：

    2025年10月1日

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  • V. A. Glazatov,
  • V. Zh. Sakbaev

摘要

We study Hamiltonian systems whose trajectories can go to infinity of the phase space in a finite time. An extension of the phase space and a set of extensions of the Hamiltonian system trajectories to the extended space are defined. Each of these extensions specifies a Hamiltonian flow in the extended space. Using a flow-invariant measure on the extended space, a representation of the Hamiltonian flow by a unitary group is obtained. The ambiguity of the extension is parameterized by a probability space, and an averaged extension is found.