Abstract:
Sufficiently high renormalizations of infinitely renormalizable
smooth mappings of the interval have extensions to quasiregular,
polynomial-like maps with small dilatation. Complex bounds for these maps
give us a new way to study the dynamics of smooth mappings on the interval.
I will talk about some progress in understanding the dynamics of these
quasiregular maps. This is joint work with Sebastian van Strien and Edson
de Faria.