Duke Mathematical Journal

Geodesics of Hofer’s metric on the group of Hamiltonian diffeomorphisms

Misha Bialy and Leonid Polterovich
Source: Duke Math. J. Volume 76, Number 1 (1994), 273-292.
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Primary Subjects: 58F05
Secondary Subjects: 58D05
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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077286745
Mathematical Reviews number (MathSciNet): MR1301192
Zentralblatt MATH identifier: 0819.58006
Digital Object Identifier: doi:10.1215/S0012-7094-94-07609-6

References

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Mathematical Reviews (MathSciNet): MR93c:58066
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Digital Object Identifier: doi:10.1007/BF01896972
[BP2] M. Bialy and L. Polterovich, Hamiltonian systems, Lagrangian tori and Birkhoff's theorem, Math. Ann. 292 (1992), no. 4, 619–627.
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Digital Object Identifier: doi:10.1007/BF01444639
[BP3] M. Bialy and L. Polterovich, Optical Hamiltonian functions, Geometry in partial differential equations eds. A. Prastaro and T. Rassias, World Sci. Publishing, River Edge, NJ, 1994, pp. 32–50.
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[H1] H. Hofer, On the topological properties of symplectic maps, Proc. Roy. Soc. Edinburgh Sect. A 115 (1990), no. 1-2, 25–38.
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[H2] H. Hofer, Estimates for the energy of a symplectic map, Comment. Math. Helv. 68 (1993), no. 1, 48–72.
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[HZ] H. Hoffer and E. Zehnder, Lectures on symplectic invariants and Hamiltonian dynamics, preprint, 1993.
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[LM2] F. Lalonde and D. McDuff, Hofer's $L^\infty$-geometry: Energy and stability of Hamiltonian flows, preprint.
[Lo] Y. Long, Geodesics in the compactly supported Hamiltonian diffeomorphisms group, preprint, 1993.
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[P] L. Polterovich, The second Birkhoff theorem for optical Hamiltonian systems, Proc. Amer. Math. Soc. 113 (1991), no. 2, 513–516.
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[U] I. Ustilovsky, Conjugate points on geodesics of Hofer's metric, manuscript, 1993.
[V] C. Viterbo, Symplectic topology as the geometry of generating functions, Math. Ann. 292 (1992), no. 4, 685–710.
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