## Dynamics, Geometry, & Groups - Alessandro Portaluri (U of Torino)

### Friday, March 22nd, 2019

**Time:** 10:30 a.m** Place:** Jeffery Hall 102

**Speaker:** Alessandro Portaluri (University of Torino, Italy)

**Title:** Visiting Kepler with a couple of symplectic friends.

**Abstract:** Starting from the classical planar Kepler problem, by using the conservation law of the angular momentum, we reduce the problem to a one degree of freedom singular problem. Thanks to this reduction and after a suitable time scaling we show that, for negative energy, the orbit is an ellipse. Finally, by using a refined version of the Conley-Zehnder intersection index , we give a homotopic classification of all bounded motions.