Dynamical Systems Seminar: Hector Lomelli

Equivariant symmetries in Poncelet maps

Hector Lomelli

Department of Mathematics, University of Texas at Austin

Date and time: 

Thursday, November 21, 2013 - 2:00pm

Location: 

ECCR 257

Abstract: 

We study symmetries of families of circle maps that arise in connection with the theorem of Poncelet.

We use the recent technique of reduction by lifting to study  diffeomorphisms that have a equivariant symmetries. Reduction by lifting can be used when a symmetry of a map is a flow with a global cross section. In that situation,  there are coordinates in which the map takes a reduced,  skew-product form and hence allows for reduction of dimensionality. In particular, we explore the possible generalizations of the classic Poncelet theorem.