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Abstract <p>The mixmaster Hořava–Lifshitz model belongs to generalized Euclidean Toda chains with 28 vectors. The longest three vectors of the spectrum play a dominant role in studying its dynamics. The truncated cosmological model is presented as a periodic three-particle Toda chain. It is associated with an affine Kac–Moody Lie algebra <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12267_2025_5273_Article_IEq1.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="23" /> </InlineMediaObject> <EquationSource Format="TEX">\(A_{2}^{+}\)</EquationSource> <!--GravCos2570019Pavlov-m1--> </InlineEquation>. According to the Adler–van Moerbeke criterion, the truncated Hamiltonian system is algebraically completely integrable. The phase curves wrap a torus of genus 2. The Jacobi problem of inversion of ultraelliptic integrals is solved by using theta-functions of two variables. The solutions of the dynamical problem are expressed in rational functions of Rosenhain theta-functions. They are four-periodic functions.</p>

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Integrability of Truncated Hořava–Lifshitz Mixmaster Model in Rosenhain Functions

  • 期刊论文

  • 发表日期：

    2025年9月4日

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  • A. E. Pavlov,
  • S. M. Gaidar

摘要

Abstract

The mixmaster Hořava–Lifshitz model belongs to generalized Euclidean Toda chains with 28 vectors. The longest three vectors of the spectrum play a dominant role in studying its dynamics. The truncated cosmological model is presented as a periodic three-particle Toda chain. It is associated with an affine Kac–Moody Lie algebra \(A_{2}^{+}\) . According to the Adler–van Moerbeke criterion, the truncated Hamiltonian system is algebraically completely integrable. The phase curves wrap a torus of genus 2. The Jacobi problem of inversion of ultraelliptic integrals is solved by using theta-functions of two variables. The solutions of the dynamical problem are expressed in rational functions of Rosenhain theta-functions. They are four-periodic functions.