Renormalization operators and Arnold tongues
Speaker:
Nataliya Goncharuk, Texas A&M University
Date and Time:
Monday, August 21, 2023 - 11:00am to 12:00pm
Location:
Fields Institute, Room 230
Abstract:
Many studies in circle dynamics are devoted to Arnold tongues: level sets of rotation numbers in parametric families of circle maps.
In analytic families of circle diffeomorphisms, Arnold tongues that correspond to Herman rotation numbers are analytic curves (E.Risler, 1999).
In contrast to this result, Llave and Luque observed in 2011 using numerical investigations that these Arnold tongues are only finitely smooth near critical circle maps.
With M.Yampolsky, we provided explanations of these effects in terms of renormalization operators.
I am going to outline main ideas of our proofs.