SMS scnews item created by Lachlan Smith at Fri 16 Oct 2020 1630
Type: Seminar
Distribution: World
Expiry: 11 Dec 2020
Calendar1: 23 Oct 2020 1600-1700
CalLoc1: Zoom
Auth: lachlans@105.66.233.220.static.exetel.com.au (lsmi9789) in SMS-WASM

# Sydney Dynamics Group: Corey Shanbrom -- Self-similarity in the Kepler-Heisenberg problem

Dear all,

Next week, Friday October 23, Corey Shanbrom (Sacramento State University) will give a
talk at 4pm (Sydney time) via Zoom.

Meeting ID: 857 2003 8635

Title: Self-similarity in the Kepler-Heisenberg problem

Abstract:
The Kepler-Heisenberg problem is that of determining the motion of a planet around a sun
in the Heisenberg group, thought of as a three-dimensional sub-Riemannian manifold.  The
sub-Riemannian Hamiltonian provides the kinetic energy, and the gravitational potential
is given by the fundamental solution to the sub-Laplacian.  The dynamics are at least
partially integrable, possessing two first integrals as well as a dilational momentum
which is conserved by orbits with zero energy.  The system is known to admit closed
orbits of any rational rotation number, which all lie within the fundamental zero energy
integrable subsystem.  Here, we demonstrate that all zero energy orbits are
self-similar.

Past talks can be found on the YouTube channel: