The Exponential Map Near Conjugate Points In 2D Hydrodynamics

The Exponential Map Near Conjugate Points In 2D Hydrodynamics

We prove that the weak-Riemannian exponential map of the L 2 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...

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Bibliographic Details
Published in:Arnold mathematical journal Vol. 1; no. 3; pp. 243 - 251
Main Author: Misiołek, Gerard
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 01-09-2015
Subjects:
Mathematics
Mathematics and Statistics
Research Contribution
46T05
Primary 58B25
Fredholm map
35Q35
Exponential map
Conjugate points
Diffeomorphisms
Secondary 37K65
Online Access:Get full text
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Summary:We prove that the weak-Riemannian exponential map of the L 2 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.
ISSN:2199-6792
2199-6806
DOI:10.1007/s40598-015-0019-1