1. Periodic Magnetic Geodesics on Heisenberg Manifolds
- Author
-
Epstein, Jonathan, Gornet, Ruth, and Mast, Maura B.
- Subjects
Mathematics - Differential Geometry ,Mathematics - Dynamical Systems - Abstract
We study the dynamics of magnetic flows on Heisenberg groups. Let $H$ denote the three-dimensional simply connected Heisenberg Lie group endowed with a left-invariant Riemannian metric and an exact, left-invariant magnetic field. Let $\Gamma$ be a lattice subgroup of $H,$ so that $\Gamma\backslash H$ is a closed nilmanifold. We first find an explicit description of magnetic geodesics on $H$, then determine all closed magnetic geodesics and their lengths for $\Gamma \backslash H$. We then consider two applications of these results: the density of periodic magnetic geodesics and marked magnetic length spectrum rigidity., Comment: 32 pages
- Published
- 2020