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Abstract <p>We study billiards in a gravitational field on a flat table bounded by arcs of confocal parabolas. Depending on the shape of the table, bifurcation diagrams are constructed and bifurcations of Liouville tori corresponding to their arcs are described. For nonsingular energy zones, the Fomenko–Zieschang invariants are calculated.</p>

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Topology of the Liouville Foliation for an Integrable Billiard Bounded by Parabolas and Having a Gravitational Potential

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • V. V. Vedyushkina,
  • A. V. Zaytseva

摘要

Abstract

We study billiards in a gravitational field on a flat table bounded by arcs of confocal parabolas. Depending on the shape of the table, bifurcation diagrams are constructed and bifurcations of Liouville tori corresponding to their arcs are described. For nonsingular energy zones, the Fomenko–Zieschang invariants are calculated.