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Seminario Especial de Matemáticas Aplicadas

Equivariant symmetries in Poncelet maps


por el

Dr. Héctor Lomelí

University of Colorado and University of Texas at Austin

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.

Jueves 22 de mayo, 2014
17:00 hrs.
Salón: 203, Edificio Anexo, IIMAS

Informes: coloquiomym@gmail.com, o al 5622-3564.