scholarly journals On the group of almost periodic diffeomorphisms

2017 ◽  
Author(s):  
Sun
Keyword(s):  
Almost Periodic ◽  
Periodic Diffeomorphisms

On the Group of Almost Periodic Diffeomorphisms and its Exponential Map

2019 ◽  
Author(s):  
Xu Sun ◽  
Peter Topalov
Keyword(s):  
Lie Group ◽  
Riemannian Metric ◽  
Conjugate Points ◽  
Exponential Map ◽  
Almost Periodic ◽  
Exponential Maps ◽  
Fluid Equations ◽  
Periodic Diffeomorphisms

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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