The Exponential Map Near Conjugate Points In 2D Hydrodynamics

被引：0
作者：
Misiołek G. [1 ,2 ]
机构：
[1] Department of Mathematics, University of Colorado, Boulder, 80309-0395, CO
[2] Department of Mathematics, University of Notre Dame, Notre Dame, 46556, IN
来源：
Arnold Mathematical Journal | 2015年 / 1卷 / 3期
关键词：
Conjugate points; Diffeomorphisms; Exponential map; Fredholm map;
D O I：
10.1007/s40598-015-0019-1
中图分类号：
学科分类号：
摘要：
We prove that the weak-Riemannian exponential map of the L2 metric on the group of volume-preserving diffeomorphisms of a compact two-dimensional manifold is not injective in any neighbourhood of its conjugate vectors. This can be viewed as a hydrodynamical analogue of the classical result of Morse and Littauer. © 2015, Institute for Mathematical Sciences (IMS), Stony Brook University, NY.
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页码：243 / 251
页数：8
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