On the group of A-P diffeomorphisms and its exponential map

Xu Sun; Peter Topalov

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arXiv · 1808.01414

On the group of A-P diffeomorphisms and its exponential map

Xu Sun·Peter Topalov

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Abstract

We define the group of almost periodic diffeomorphisms on $\mathbb{R}^n$ and on an arbitrary Lie group. We then study the properties of its Riemannian and Lie group exponential maps and provide applications to fluid equations. In particular, we show that there exists a geodesic of a weak Riemannian metric on the group of almost periodic diffeomorphisms of the line that consists entirely of conjugate points.

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Xu Sun, Peter Topalov. 2018-08-04. On the group of A-P diffeomorphisms and its exponential map. https://arxiv.org/abs/1808.01414

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