On the Group of Almost Periodic Diffeomorphisms and its Exponential Map-Reference-Cited by-同舟云学术

On the Group of Almost Periodic Diffeomorphisms and its Exponential Map

Published:2019-08-21 Issue:13 Volume:2021 Page:9648-9716
ISSN:1073-7928
Container-title:International Mathematics Research Notices
language:en
Short-container-title:

Author:

Sun Xu¹,Topalov Peter¹

Affiliation:

1. Department of Mathematics, Northeastern University, Boston, MA 02115, USA

Abstract

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.

Funder

Simons Foundation

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Link

http://academic.oup.com/imrn/article-pdf/2021/13/9648/40358180/rnz155.pdf

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