Espaces de Krein et index des systèmes hamiltoniens

V. Brousseau

Annales de l'I.H.P. Analyse non linéaire (1990)

  • Volume: 7, Issue: 6, page 525-560
  • ISSN: 0294-1449

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Brousseau, V.. "Espaces de Krein et index des systèmes hamiltoniens." Annales de l'I.H.P. Analyse non linéaire 7.6 (1990): 525-560. <http://eudml.org/doc/78238>.

@article{Brousseau1990,
author = {Brousseau, V.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {Hamiltonian systems; Hilbert product; resolvant; symplectic operator; Krein product; normal operator; Krein determinant; Krein trace; index},
language = {fre},
number = {6},
pages = {525-560},
publisher = {Gauthier-Villars},
title = {Espaces de Krein et index des systèmes hamiltoniens},
url = {http://eudml.org/doc/78238},
volume = {7},
year = {1990},
}

TY - JOUR
AU - Brousseau, V.
TI - Espaces de Krein et index des systèmes hamiltoniens
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1990
PB - Gauthier-Villars
VL - 7
IS - 6
SP - 525
EP - 560
LA - fre
KW - Hamiltonian systems; Hilbert product; resolvant; symplectic operator; Krein product; normal operator; Krein determinant; Krein trace; index
UR - http://eudml.org/doc/78238
ER -

References

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  1. [AG] N.I. Achieser et I.M. Glasman, Theorie der linearen Operatoren im Hilbert-Raum, Akademie Verlag, Berlin, 1975. Zbl0308.47001MR66560
  2. [Be] A. Bensoussan, Stochastic Control byFunctional Analysis Methods, North Holland, 1982. Zbl0474.93002MR652685
  3. [Br1] V. Brousseau, L'index d'un système hamiltonien linéaire, C. R. Acad. Sci. Paris, série I, n° 8, 1986, p. 351-354. Zbl0592.58022MR860837
  4. [Br2] V. Brousseau, D.P. n° 8809 du Ceremade. 
  5. [CZ] C. Conley et E. Zehnder, Morse-type index for flows and periodic solutions for Hamiltonian equations, Comm. P.A.M., vol. 37, 1984, p. 207-253. Zbl0559.58019MR733717
  6. [E1] I. Ekeland, Une théorie de Morse pour les systèmes hamiltoniens convexes, Ann. Inst. Henri-Poincaré, Analyse non linéaire, vol. 1, 1984, p. 19-78. Zbl0537.58018MR738494
  7. [E2] I. Ekeland, An index theory for periodic solutions of convex hamiltonian systems, Nonlinear Functional Analysis and its Applications, Proc. Symp. Pure Math., vol. 45, 1986, p. 395-423. Zbl0596.34023MR843575
  8. [L1] H. Langer, Spehtraltheorie linearer Operatoren in J-Raümen und einige Anwerdungen auf die Schar L(λ)=λ2I+λB+C, Thèse d'Habilitation, Technische Unversität Dresden, 1965. 
  9. [L2] H. Langer, Invariante Teilraüme definisierbarer J-selbst-adjungreiten Operatoren, Ann. Acad. Sci. Fenn. Ser. AI, vol. 475, 1971. Zbl0232.47009MR287347
  10. [KL] M.G. Krein et H. Langer, Sur la fonction spectrale d'un opérateur autoadjoint dans un espace à métrique indéfinie (en russe), Dokl. Akad. Nauk. S.S.S.R., vol. 152, 1963, p. 39-42. Zbl0131.12604
  11. [YS] V. Yakubovick et V. Starzhinski, Linear differential equations with periodic coefficients, Halsted Press, Wiley, 1975. Zbl0308.34001

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