Propriétés génériques de l'application de Poincaré et des géodésiques périodiques généralisées

V. M. Petkov; L. N. Stojanov

Séminaire Équations aux dérivées partielles (Polytechnique) (1985-1986)

  • page 1-12

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Petkov, V. M., and Stojanov, L. N.. "Propriétés génériques de l'application de Poincaré et des géodésiques périodiques généralisées." Séminaire Équations aux dérivées partielles (Polytechnique) (1985-1986): 1-12. <http://eudml.org/doc/111886>.

@article{Petkov1985-1986,
author = {Petkov, V. M., Stojanov, L. N.},
journal = {Séminaire Équations aux dérivées partielles (Polytechnique)},
keywords = {lemma of Poincaré; periodic geodesics; rays reflections},
language = {fre},
pages = {1-12},
publisher = {Ecole Polytechnique, Centre de Mathématiques},
title = {Propriétés génériques de l'application de Poincaré et des géodésiques périodiques généralisées},
url = {http://eudml.org/doc/111886},
year = {1985-1986},
}

TY - JOUR
AU - Petkov, V. M.
AU - Stojanov, L. N.
TI - Propriétés génériques de l'application de Poincaré et des géodésiques périodiques généralisées
JO - Séminaire Équations aux dérivées partielles (Polytechnique)
PY - 1985-1986
PB - Ecole Polytechnique, Centre de Mathématiques
SP - 1
EP - 12
LA - fre
KW - lemma of Poincaré; periodic geodesics; rays reflections
UR - http://eudml.org/doc/111886
ER -

References

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  1. [1] K. Andersson and R. Melrose, The propagation of singularities along gliding rays, Invent. Math., 41, (1977), p.197-232. Zbl0373.35053MR494322
  2. [2] M. Golubitsny and V. Guillemin, Stable mappings and their singularitiesSpringer, New York, 1973. Zbl0294.58004MR341518
  3. [3] V. Guillemin, Sojourn time and asymptotic properties of the scattering matrix, Publ. R.I.M.S.Kyoto Univ.12, Supl., (1977), p.69-88. Zbl0381.35064MR448453
  4. [4] V. Guillemin and R. Melrose, The Poisson summation formula for manifolds with boundary, Adv. in Math., 32, (1979), p.204-232. Zbl0421.35082MR539531
  5. [5] W. Klingenberg and F. Takens, Generic properties of geodesic flows, Math., Ann., 197, (1972), p. 323-334. Zbl0225.58006MR307282
  6. [6] V.F. Lazutkin, Convex billiard and eigenfunctions of the Laplace operator, Ed. Leningrad University, 1981, (in Russian). Zbl0532.58031MR633153
  7. [7] R. Melrose and I. Sjöstrand, Singularities in boundary value problems I, II, Comm. Pure Appl. Math., 31, (1978), p.593-617 and 35, (1982), p. 129-168. Zbl0368.35020
  8. [8] V. Petkov, Propriétés génériques des rayons réfléchissants et applications aux problèmes spectraux, Séminaire Bony-Sjöstrand-Meyer, Ecole Polytechnique, Centre de Mathématiques, Exposé XII, 1984-1985. Zbl0597.35092MR819778
  9. [9] V. Petkov, High frequency asymptotics of the scattering amplitude for non-convex bodies, Comm. in Partial Diff. Equations, 5, (1980), p.293-329. Zbl0435.35065MR562545
  10. [10] V. Petkov, Note on the distribution of poles of the scattering matrix, J. Math. Anal. Appl., 101, (1984), p.582-587. Zbl0562.35065MR748591
  11. [11] V. Petkov et P. Vogel, La représentation de l'application de Poincaré correspondant aux rayons périodiques réfléchissants, C.R. Acad. Sci. Paris, Ser.A, 296, (1983), p.633-635. Zbl0543.35004MR705678
  12. [12] V. Petkov and L. Stojanov, Periods of multiple reflecting rays and inverse spectral results, preprint. 
  13. [13] V. Petkov and L. Stojanov, Generic properties of the spectrum of the Poincaré map for multiple reflecting rays, preprint. Zbl0611.58048
  14. [14] V. Petkov and L. Stojanov, Sojourn time for reflecting scattered rays, preprint. 
  15. [15] L. Stojanov, Generic properties of periodic reflecting rays, preprint. Zbl0619.58030MR922367
  16. [16] L. Stojanov, Generic properties of scattered rays, C.R. Acad. Sci. Bulg. (to appear). Zbl0605.58045MR868703

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