Work

Integrability of the magnetic geodesic flow on the sphere with a constant 2-form

Year: 2025

Type: article

Abstract: In this paper, we prove a recent conjecture of [V. Dragović, B. Gajić and B. Jovanović, Integrability of homogeneous exact magnetic flows on spheres, Regul. Chaotic Dyn. 30(4) (2025) 582–597, doi:10.1134/S1560354725040082] stating that the magnetic geodesic flow on the standard sphere [Formula: see text] whose magnetic 2-form is the restriction of a constant 2-form from [Formula: see text] is Liouville integrable. The integrals are quadratic and linear in momenta.

Source: International Journal of Geometric Methods in Modern Physics

DOI: 10.1142/s0219887826500416

Authors: Alexey V. Bolsinov, Andrey Yu. Konyaev, Vladimir S. Matveev

Institutions: Loughborough University, Institute of Mathematics and Mathematical Modeling, Lomonosov Moscow State University, Moscow Center of Fundamental and Applied Mathematics, Friedrich Schiller University Jena

Language: English

Topic: Advanced Differential Geometry Research

Subfield: Astronomy and Astrophysics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funders: Deutsche Forschungsgemeinschaft, Ministry of Education and Science of the Republic of Kazakhstan, Australian Research Council

Awards: Nijenhuisgeometrie: singuläre Punkte und Anwendungen, Finite dimensional integrable systems and differential geometry, Polynomielle Integrabilität von natürlichen zweidimensionalen Hamiltonischen Systemen und deren Anwendungen, G7618626607