On the group of almost periodic diffeomorphisms

• Online Access: http://hdl.handle.net/2047/D20260858

In this thesis we define and study the main properties of the group of almost periodic diffeomorphisms of Rⁿ. Using these properties, we then prove that the Camassa-Holm equation and a multi-dimensional version of it are locally well-posed in the space of almost periodic functions. Further, we study the Riemannian exponential map corresponding to a right-invariant (weak) Riemannian metric on the Frechet-Lie group of almost periodic diffeomorphisms $\em Diff^{\infty}{\em ap}(\mathbb{Rⁿ})$. We prove that the corresponding Riemannian exponential map is a local diffeomorphism onto an open neighborhood of the identity in $\em Diff^{\infty}{\em ap}(\mathbb{Rⁿ})$.