Homogeneity of magnetic trajectories in the Berger sphere

Abstract

We study the homogeneity of contact magnetic trajectories in naturally reductive Berger spheres. We prove that every contact magnetic trajectory is a product of a homogeneous geodesic and a charged Reeb flow.

arXiv comment37 pages

References in corpus (9)

• Integrable geodesic flow with positive topological entropy
• Integrable magnetic geodesic flows on Lie groups
• Two-step homogeneous geodesics in homogeneous spaces
• The smallest Laplace eigenvalue of homogeneous 3-spheres
• Unimodular Sasaki and Vaisman Lie groups
• On the existence of critical compatible metrics on contact $3$-manifolds
• Motion of charged particle in a class of homogeneous spaces
• Homogeneity of magnetic trajectories in the real special linear group
• Jacobi relations on naturally reductive homogeneous spaces

Cited by in corpus (1)

• Contact magnetic geodesic and sub-Riemannian flows on $V_{n,2}$ and integrable cases of a heavy rigid body with a gyrostat