Liouville classification of integrable geodesic flows on a projective plane in a potential field

TL;DR

This paper classifies integrable geodesic flows on a projective plane with a potential, using Liouville theory and computes all associated Fomenko--Zieschang invariants.

Contribution

It provides a complete Liouville classification and calculates all Fomenko--Zieschang invariants for this specific Hamiltonian system.

Findings

Complete classification of the system's Liouville foliation

Explicit calculation of all Fomenko--Zieschang invariants

Advancement in understanding integrable flows on non-orientable surfaces

Abstract

A Liouville classification of a natural Hamiltonian system on the projective plane with a rotation metric and a linear integral is obtained. All Fomenko--Zieschang invariants (i.e., labeled molecules) of the system are calculated.