Renormalization and rigidity for circle maps with singularities

Speaker: Konstantin Khanin (BIMSA)

Abstract: I shall explain the main ideas of the renormalization theory in the setting of circle maps.

In the cases when convergence of renormalization is established one can prove important rigidity results. In the simplest case of circle diffeomorphisms rigidity is equivalent to the Herman theory which states that under certain Diophantine-type conditions smooth circle diffeomorphisms with irrational rotation numbers can be smoothly linearized. This case corresponds to very simple renormalization dynamics. Namely, renormalized maps converge to linear maps with slope1.

Much richer and more interesting renormalization behavior can be observed for circle maps with singularities. The main examples are provided by critical circle maps and circle maps with breaks. In this talk I will present the main results on renormalization and rigidity in all three settings described above.

Time: 16:00, Thursday, Nov. 14, 2024

Location: Room 1210, SIMIS, Block A, No. 657 Songhu Road, Yangpu District, Shanghai