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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
     

Conjugate points in ${\mathcal D}_{\mu}(T^2)$

Author(s): Gerard Misiolek
Journal: Proc. Amer. Math. Soc. 124 (1996), 977-982.
MSC (1991): Primary 58B20, 58D05; Secondary 76E99
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Abstract | References | Similar articles | Additional information

Abstract: An example of a geodesic in ${\mathcal D}_{\mu}(T^2)$ with conjugate points is given, thus providing an affirmative answer to a question of V.I. Arnol$'$d.


References:

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V. I. Arnol$'$d, Sur la geometrie differentielle des groupes de Lie de dimension infinie et ses applications a l'hydrodynamique des fluids parfaits, Ann. Inst. Grenoble 16 (1966).MR 34:1956

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J. Cheeger and D. Ebin, Comparison theorems in Riemannian geometry, North-Holland, New York, 1975.MR 56:16538

[DFGHMS]
T. Dombre, U. Frisch, J. M. Greene, M. Henon, A. Mehr, and A. M. Soward, Chaotic streamlines in the ABC flows, J. Fluid Mech. 167 (1986).

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D. Ebin and J. Marsden, Groups of diffeomorphisms and the motion of an incompressible fluid, Ann. of Math. (2) 92 (1970).MR 42:6865

[FGV]
S. Friedlander, A. Gilbert, and M. Vishik, Hydrodynamic instability for certain ABC flows, preprint.

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N. Grossman, Hilbert manifolds without epiconjugate points, Proc. Amer. Math. Soc. 16 (1965).MR 32:6370

[M]
G. Misio{\l}ek, Stability of flows of ideal fluids and the geometry of the group of diffeomorphisms, Indiana Univ. Math. J. 42 (1993). MR 94j:58027

[Y]
K. Yosida, Functional analysis, 6th ed., Springer-Verlag, New York, 1980.


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Additional Information:

Gerard Misiolek
Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
Email: misiolek.1@nd.edu

DOI: 10.1090/S0002-9939-96-03149-8
PII: S 0002-9939(96)03149-8
Keywords: Conjugate points, diffeomorphism groups
Received by editor(s): January 24, 1994
Received by editor(s) in revised form: September 16, 1994
Communicated by: Barbara Lee Keyfitz
Copyright of article: Copyright 1996, American Mathematical Society


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