Abstract: One of the least understood class of quadratic maps are in nitely renormalizable polynomial-like maps of satellite type. In this talk we discuss the geometric structure of the post-critical sets of in nitely satellite renormalizable maps of high type using near-parabolic renormalization. Notably, we identify an optimal arithmetic condition leading to a weak form of a priori bounds property for the polynomial-like renormalizations. This notion is slightly weaker than a priori bounds, but still implies many deep results on the dynamics of the corresponding maps such as ergodic behaviour. The talk is based on a joint work with Cheraghi.
For further information please see the Dynamical Systems website