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An inverse problem of Hamiltonian dynamics


Authors: M. Rudnev and V. Ten
Journal: Proc. Amer. Math. Soc. 134 (2006), 3295-3299
MSC (2000): Primary 37J05, 70H12
DOI: https://doi.org/10.1090/S0002-9939-06-08351-1
Published electronically: May 8, 2006
MathSciNet review: 2231914
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Abstract: We study the question of whether for a natural Hamiltonian system on a two-dimensional compact configuration manifold, a single trajectory of sufficiently high energy is almost surely enough to reconstruct a real analytic potential.


References [Enhancements On Off] (What's this?)

  • 1. A. Besse. Manifolds all of whose Geodesics are Closed. Springer-Verlag, Berlin, Heidelberg, New York, 1978. MR 0496885 (80c:53044)
  • 2. A.V. Bolsinov, B. Jovanovic. Noncommutative integrability, moment map and geodesic flows. Ann. Global Anal. Geom. 23 (2003), no. 4, 305-322. MR 1972543 (2004b:37113)
  • 3. V.I. Arnold, V.V. Kozlov, A.I. Neishtadt. Encyclopedia of Mathematical Sciences. Dynamical Systems III. Mathematical Aspects of Classical and Celestial Mechanics. Springer-Verlag, Berlin, 1988.MR 1292466 (95d:58043b)
  • 4. L.W. Green. Auf Wiedersehensflächen. Ann. of Math. 78 (1963), no. 2, 289-299.MR 0155271 (27:5206)
  • 5. M. de León, P.R. Rodrigues. Methods of differential geometry in analytical mechanics. North-Holland Mathematics Studies 158. North-Holland Publishing Co., Amsterdam, 1989. MR 1021489 (91c:58041)
  • 6. V.V. Ten. Analytic invariants of dynamical systems with positive entropy. (Russian). Vestnik Moskov. Univ. Ser. I Mat. Mekh. (1997), no. 3, 40-43.MR 1483040 (98g:58107)
  • 7. J.A. Yorke. Periods of periodic solutions and the Lipschitz constant. Proc. Amer. Math. Soc. 22 (1969), 509-512. MR 0245916 (39:7222)
  • 8. O. Zoll. Über Flächen mit Scharen geschlossener geodätischer Linien. (German). Math. Ann. 57 (1903), 108-133. MR 1511201

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Additional Information

M. Rudnev
Affiliation: Department of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, United Kingdom
Email: m.rudnev@bris.ac.uk

V. Ten
Affiliation: Department of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, United Kingdom
Email: v.ten@bris.ac.uk

DOI: https://doi.org/10.1090/S0002-9939-06-08351-1
Received by editor(s): February 14, 2005
Received by editor(s) in revised form: May 26, 2005
Published electronically: May 8, 2006
Communicated by: Carmen C. Chicone
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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