Dynamics Seminar

Event Information Renormalization of critical circle maps with a critical point of order close to 3
15:10 on Monday October 20, 2014
16:00 on Monday October 20, 2014
BA6183, Bahen Center, 40 St. George St.
Igors Gorbovickis

University of Toronto

The universality phenomena in smooth families of circle homeomorphisms with one critical point, the so-called critical circle maps, are analogous to Feigenbaum universality and are explained by hyperbolicity of the so-called cylinder renormalization operator. So far the theory is complete only in the case of critical circle maps with the critical point of order $3$ (or any other odd positive integer). In this talk I will extend the cylinder renormalization operator to the new functional space that includes critical circle maps with the critical point of an arbitrary order. Then applying perturbation argument, I will show that in the space of critical circle maps of bounded type and with the critical point of a fixed order close to 3, the periodic orbits of the cylinder renormalization operator are hyperbolic.

This is a joint work with Michael Yampolsky.