Analyticity of Riemannian exponential maps on ${\rm Diff}(\T)$

Abstract

We study the exponential maps induced by Sobolev type right-invariant (weak) Riemannian metrics of order $k\ge 1$ on the Lie group of smooth, orientation preserving diffeomorphisms of the circle. We prove that each of them defines an {\em analytic} Fréchet chart of the identity.