IIMAS - FENOMEC
UNAM
Equivariant symmetries in Poncelet maps
Resumen:
We study symmetries of families of circle maps that arise in connection
with the classic theorem of Poncelet. We use the recent technique of reduction by lifting to study diffeomorphisms that have 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, a covering space is introduced. As a consequence, we prove the existence of coordinates in which the map
takes a reduced, skew-product form and hence allows for reduction of dimensionality. In the Poncelet theorem, the rotation number plays an important role and our reduction by lifting produces a simple formula in terms of elliptic functions. We also explore possible generalizations.
Informes: coloquiomym@gmail.com, o al 5622-3564.