Conjugate points in $\mathcal {D}_{\mu }(T^2)$
HTML articles powered by AMS MathViewer
- by Gerard Misiolek
- Proc. Amer. Math. Soc. 124 (1996), 977-982
- DOI: https://doi.org/10.1090/S0002-9939-96-03149-8
- PDF | Request permission
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
- V. Arnold, Sur la géométrie différentielle des groupes de Lie de dimension infinie et ses applications à l’hydrodynamique des fluides parfaits, Ann. Inst. Fourier (Grenoble) 16 (1966), no. fasc. 1, 319–361 (French). MR 202082
- Jeff Cheeger and David G. Ebin, Comparison theorems in Riemannian geometry, North-Holland Mathematical Library, Vol. 9, North-Holland Publishing Co., Amsterdam-Oxford; American Elsevier Publishing Co., Inc., New York, 1975. MR 0458335
- 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).
- David G. Ebin and Jerrold Marsden, Groups of diffeomorphisms and the motion of an incompressible fluid, Ann. of Math. (2) 92 (1970), 102–163. MR 271984, DOI 10.2307/1970699
- S. Friedlander, A. Gilbert, and M. Vishik, Hydrodynamic instability for certain ABC flows, preprint.
- Nathaniel Grossman, Hilbert manifolds without epiconjugate points, Proc. Amer. Math. Soc. 16 (1965), 1365–1371. MR 188943, DOI 10.1090/S0002-9939-1965-0188943-7
- Gerard Misiołek, Stability of flows of ideal fluids and the geometry of the group of diffeomorphisms, Indiana Univ. Math. J. 42 (1993), no. 1, 215–235. MR 1218713, DOI 10.1512/iumj.1993.42.42011
- K. Yosida, Functional analysis, 6th ed., Springer-Verlag, New York, 1980.
Bibliographic Information
- Gerard Misiolek
- Affiliation: Department of Mathematics University of Notre Dame Notre Dame, Indiana 46556
- Email: misiolek.1@nd.edu
- Received by editor(s): January 24, 1994
- Received by editor(s) in revised form: September 16, 1994
- Communicated by: Barbara Lee Keyfitz
- © Copyright 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 124 (1996), 977-982
- MSC (1991): Primary 58B20, 58D05; Secondary 76E99
- DOI: https://doi.org/10.1090/S0002-9939-96-03149-8
- MathSciNet review: 1301038