Integrability of moduli and regularity of Denjoy counterexamples

08.10.2019 15:00 - 17:00

Sang-hyun Kim (KIAS)

We study the regularity of finitely generated group actions on the circle by \(C^1\)-diffeomorphisms with wandering intervals. A classical theorem of Denjoy prohibits such actions from being \(C^2\). We prove that under a mild technical condition, if a concave modulus of continuity \(a(x)\) satisfies that \(1/a(x)^d\) is integrable near 0, then \(Z^d\) (or a group with its spherical growth function bounded by \(Cn^{d-1}\)) admits a \(C^{1,a}\) action on the circle with wandering intervals. We also discuss a partial converse to this result. This is  a joint work with Thomas Koberda.


G. Arzhantseva, Ch. Cashen


SR 7, 2. OG., OMP 1