Modul:   MAT760  Ergodic theory and dynamical systems seminar

Some recent results on multicritical circle maps

Vortrag von Dr. Gabriela Estevez

Sprecher eingeladen von: Prof. Dr. Corinna Ulcigrai

Datum: 02.10.23  Zeit: 15.00 - 16.00  Raum: Y27H25

In 1984 Yoccoz proved that any two C^3 orientation-preserving circle homeomorphisms, with the same quantity of non-flat critical points and the same irrational rotation number, are topologically conjugated. For maps with only one critical point, it has been shown that the conjugacy is, in fact, a C^1-diffeomorphism. Moreover, in a total Lebesgue measure set of irrational rotation numbers the conjugacy can be improved to be C^{1+\alpha}. In this talk, we will discuss some recent results concerning the smoothness of the conjugacy for maps with more than one critical point, and how these results are obtained using renormalization.''