Lagrange schwarzian derivative and symplectic Sturm theory

Valentin Ovsienko

Annales de la Faculté des sciences de Toulouse : Mathématiques (1993)

  • Volume: 2, Issue: 1, page 73-96
  • ISSN: 0240-2963

How to cite

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Ovsienko, Valentin. "Lagrange schwarzian derivative and symplectic Sturm theory." Annales de la Faculté des sciences de Toulouse : Mathématiques 2.1 (1993): 73-96. <http://eudml.org/doc/73314>.

@article{Ovsienko1993,
author = {Ovsienko, Valentin},
journal = {Annales de la Faculté des sciences de Toulouse : Mathématiques},
keywords = {multidimensional Lagrange-Schwarzian derivative; linear differential equations; loop groups; linear symplectic space; Newton equations; nonoscillation condition},
language = {eng},
number = {1},
pages = {73-96},
publisher = {UNIVERSITE PAUL SABATIER},
title = {Lagrange schwarzian derivative and symplectic Sturm theory},
url = {http://eudml.org/doc/73314},
volume = {2},
year = {1993},
}

TY - JOUR
AU - Ovsienko, Valentin
TI - Lagrange schwarzian derivative and symplectic Sturm theory
JO - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY - 1993
PB - UNIVERSITE PAUL SABATIER
VL - 2
IS - 1
SP - 73
EP - 96
LA - eng
KW - multidimensional Lagrange-Schwarzian derivative; linear differential equations; loop groups; linear symplectic space; Newton equations; nonoscillation condition
UR - http://eudml.org/doc/73314
ER -

References

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  2. [A2] Arnold ( V.I.) .— Sturm theorems and symplectic geometry, Function Anal. and its Appl.19, n° 1 (1985), pp. 1-10. Zbl0606.58017MR820079
  3. [A3] Arnold ( V.I.) . — On a characteristic class intervening in quantization conditions, Funct. Anal. and its Appl.1, n° 1 (1967), pp. 1-14. Zbl0175.20303MR211415
  4. [B] Bott ( R.) . — On the iterations of closed geodesics and the Sturm intersection theory, Comm. Pure Appl. Math.9, n° 2 (1956), pp. 171-206. Zbl0074.17202MR90730
  5. [Br] Brown ( K.S.) . — Buildings, Springer-Verlag (1988). 
  6. [Ca] Carne ( K.) . — The Schwarzian derivative for conformal maps, J. Reine Angew Math.408 (1990), pp. 10-33. Zbl0705.30010MR1058982
  7. [C] Coppel ( J.) . — Disconjugacy, Lect. Notes in Math.220 (1970). Zbl0224.34003
  8. [FI] Flanders ( H.) .— The Schwarzian as a curvature, J. Diff. Geometry4, n° 4, pp. 515-519. Zbl0232.53005MR276879
  9. [Fu] Fuchs ( D.B.) . — Cohomologies of infinite-dimensional Lie algebras, Consultants Bureau, New York (1986). Zbl0667.17005MR874337
  10. [Ki] Kirillov ( A.A.) . — Infinite-dimensional Lie groups: their orbits, invariants and representations. Geometry of moments, Lect. Notes in Math.970 (1982), pp. 101-123. Zbl0498.22017MR699803
  11. [Kl] Klein ( F.) . — Vorlesungen uber das ikosaeder und die auflosing der gleichungen vom funfen grade, Leipzig (1884). Zbl0803.01037JFM16.0061.01
  12. [L] Lagrange ( J.-L.) . — Sur la construction des cartes géographiques, Nouveaux Mémoires de l'Académie de Berlin (1779). 
  13. [M] Morse ( M.) . — A generalization of the Sturm theorems in n-space, Math. Ann.103 (1930), pp. 52-69. Zbl56.1078.03JFM56.1078.03
  14. [N] Nehari ( Z.) . — The Schwarzian derivative and schlicht functions, Bull. Amer. Math. Soc.55, n° 6 (1949). Zbl0035.05104MR29999
  15. [O1] Ovsienko ( V. Yu.) .— Hook Law and Denogardus Great Number, Kvant8 (1989) pp. 8-16 (Russian). 
  16. [O2] Ovsienko ( V. Yu.). — Lagrange Schwarzian derivative, Vestnik Moscow State University6 (1889), pp. 42-45 (Russian). Zbl0707.70005MR1065975
  17. [R] Royan ( J.) . — Generalised Schwarzian derivatives for generalised fractional linear transformations, Annales Polinici Math. (to appear). Zbl0762.15013
  18. [RS] Retakh ( V.) and Shander ( V.) .— Noncommutative analogues of the Schwarzian derivative, Preprint. 
  19. [T] Tabachnikov ( S.) .— Projective structures and group Vey cocycle, Preprint E.N.S. de Lyons (1992). 

Citations in EuDML Documents

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  1. S. Bouarroudj, V. Ovsienko, Schwarzian derivative related to modules of differential operators on a locally projective manifold
  2. Gloria Marí Beffa, Projective-type differential invariants and geometric curve evolutions of KdV-type in flat homogeneous manifolds
  3. Boujemaa Agrebaoui, Raja Hattab, 1 -cocycles on the group of contactomorphisms on the supercircle S 1 | 3 generalizing the Schwarzian derivative
  4. Gloria Marí Beffa, Moving frames, Geometric Poisson brackets and the KdV-Schwarzian evolution of pure spinors
  5. Boris Doubrov, Igor Zelenko, On geometry of curves of flags of constant type

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