KaydedilenlerDerginizi ekleyin

Dergiler / International Electronic Journal of Geometry / 2026 / Volume: 11 Issue: 1

Geometric Study of a Family of Integrable Systems

Ahmed Lesfari
Sayfa
—
Yayın Tarihi
2018-04-30
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

The aim of this paper is to demonstrate the rich interaction between complex algebraic geometry,

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:The aim of this paper is to demonstrate the rich interaction between complex algebraic geometry,
📊
Temel Bulgular & Veri:The aim of this paper is to demonstrate the rich interaction between complex algebraic geometry,
💡
Sonuç & Katkı:The aim of this paper is to demonstrate the rich interaction between complex algebraic geometry,
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Integrable systems · gap theory · abelian varieties

Abstract

The aim of this paper is to demonstrate the rich interaction between complex algebraic geometry,

🔖

Bu Makaleye Atıf Yap

Lesfari, A. (2018). Geometric Study of a Family of Integrable Systems. International Electronic Journal of Geometry, Volume: 11 Issue: 1. https://doi.org/10.36890/iejg.545100

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (51)

  1. Adler, M., van Moerbeke, P., Linearization of Hamiltonian systems, Jacobi varieties and representation theory. Adv. in Math. 38 (1980), 318-379.
  2. Adler, M., van Moerbeke, P., The complex geometry of the Kowalewski-Painlevé analysis. Invent. Math. 7 (1989), 3-51.
  3. Adler, M., van Moerbeke, P. and Vanhaecke, P., Algebraic integrability, Painlevé geometry and Lie algebras. A series of modern surveys in mathematics, Volume 47, Springer-Verlag, 2004.
  4. Airault. H., Mc Kean, H.P. and Moser, J., Rational and elliptic solutions of the KdV equation and a related many-body problem. Comm. Pure Appl. Math. 30 (1977), 94-148.
  5. Arnold, V.I., Mathematical methods in classical mechanics. Springer-Verlag, Berlin-Heidelberg- New York, 1978.
  6. Baker, S., Enolskii, V.Z. and Fordy, A.P., Integrable quartic potentials and coupled KdV equations. Phys. Lett. 201A (1995), 167-174.
  7. Barth, W., Abelian surfaces with (1; 2)􀀀polarization. Conf. on alg. geom., Sendai, 1985, Advanced studies in pure mathematics, 10 (1987), 41-84.
  8. Barth, W., Affine parts of abelian surfaces as complete intersections of four quadrics. Math. Ann. 278 (1987), 117-131.
  9. Belokolos, A.I. and Enol’skii, V.Z., Isospectral deformations of elliptic potentials. Russ. Math. Surveys, 44 (1989), 155-156.
  10. Belokolos, A.I., Bobenko, V.Z., Enol’skii, V.Z., Its, A.R. and Matveev, V.B., Algebro-Geometric approach to nonlinear integrable equations. Springer-Verlag 1994.
  11. Bountis, T., Segur, H. and Vivaldi, F., Integrable hamiltonian systems and the Painlevé property. Phys. Rev. A25 (1982), 1257-1264.
  12. Christiansen, P.L., Eilbeck, J.C., Enolskii, V.Z. and Kostov, N.A., Quasi-periodic solutions of the coupled nonlinear Schrödinger equations. Proc. R. Soc. Lond. A451 (1995), 685-700.
  13. Conte, R., Musette, M. and Verhoeven, C., Completeness of the cubic and quartic Hénon-Heiles hamiltonians. Theor. Math. Phys. 144 (2005), 888-898.
  14. Eilbeck, J.C., Enolskii, V.Z., Kuznetsov, V.B. and Leykin, D.V., Linear r-matrix algebra for systems separable in parabolic coordinates. Phys. Lett. 180A (1993), 208-214.
  15. Eilbeck, J.C., Enolskii, V.Z., Kuznetsov, V.B. and Tsiganov, A.V., Linear r-matrix algebra for classical separable systems. J. Phys. A.: Math. Gen. 27 (1994), 567-578.
  16. Eilbeck, J.C., Enolskii, V.Z., Elliptic solutions and blow-up in an integrable Hénon-Heiles system. Proc. Roy. Soc. Edinburgh, A124 (1994), 1151-1164.
  17. Grammaticos, B. Dorozzi, B., Ramani, A., Integrability of hamiltonians with third and fourth-degree polynomial potentials. J. Math. Phys. 24 (1983), 2289-2295.
  18. Griffiths, P.A., Harris,J., Principles of algebraic geometry.Wiley-Interscience 1978.
  19. Haine, L., Geodesic flow on SO(4) and Abelian surfaces. Math. Ann. 263 (1983), 435-472.
  20. Halphen, G. H., Mémoire sur la réduction des équations différentielles linéaires aux formes intégrales. Mémoires présentés par divers savants à l’Académie des sciences de l’Institut de France 28, 1-307, 1884.
  21. Hermite, C., Oeuvres de Charles Hermites. Vol. III, Paris, Gauthier-Villar, 1912.
  22. Hietarinta, J., Classical versus quantum integrability. J. Math. Phys. 25 (1984), 1833-1840.
  23. Hietarinta, J., Direct methods for the search of the second invariant. Phys. Rep. 147 (1987), 87-154.
  24. Kasperczuk, S., Integrability of the Yang-Mills hamiltonian system. Celes. Mech. and Dyn. Astr. 58 (1994), 387-391. Erratum Celes. Mech. and Dyn. Astr. 60 (1994), 289.
  25. Kostov, N.A., Quasi-periodical solutions of the integrable dynamical systems related to Hill’s equation. Lett. Math. Phys. 17 (1989), 95-104.
  26. Kowalewski, S., Sur le problème de la rotation d’un corps solide autour d’un point fixe. Acta Math. 12 (1889), 177-232.
  27. Lesfari, A., Abelian surfaces and Kowalewski’s top. Ann. Scient. École Norm. Sup. Paris, 4e série, t.21 (1988), 193-223.
  28. Lesfari, A., Prym varieties and applications. J. Geom. Phys., 58, 1063-1079 (2008).
  29. Lesfari, A., Integrable systems and complex geometry. Lobachevskii Journal of Mathematics, Vol.30, No.4, 292-326 (2009).
  30. Lesfari, A.: Algebraic integrability: the Adler-van Moerbeke approach. Regul. Chaotic Dyn. 16 (2011), Nos.3-4, pp.187-209.
  31. Lesfari, A., Introduction à la géométrie algébrique complexe. Hermann, Paris 2015.
  32. McKean, H.P. and van Moerbeke, P., The Spectrum of Hill’s Equation. Invent. Math. 30 (1975), 217-274.
  33. Moser, J., Three integrable Hamiltonian systems connected with isospectral deformations. Adv. Math. 16 (1975), 197-219.
  34. Moser, J., Geometry of quadrics and spectral theory. Lecture delivred at the symposium in honor of S.S. Chern, Berkeley, 1979. Springer, Berlin, Heidelberg, New-York 1980.
  35. Mumford, D., On the equations defining abelian varieties I, II, III. Invent. Math. 1 (1966), 287-354, 3 (1967), 75-135, 3 (1967), 215-244.
  36. Mumford, D., Tata lectures on theta I, II. Progress in mathematics. Birkhaüser, Boston, 1983.
  37. Novikov, S.P., The periodic problem for Korteweg-de Vries equation. Funct. Anal. Pril. 8 (1974), 53-66.
  38. Perelomov, A.M., Integrable systems of classical mechanics and Lie algebras. Birkhäuser Verlag 1990.
  39. Ravoson, V., Ramani, A. and Grammaticos, B., Generalized separability for a hamiltonian with nonseparable quartic potential. Phys. Lett. 191A (1994), 91-95.
  40. Smirnov, A. O., Finite-gap elliptic solutions of the KdV equation. Acta Appl. Math. 36 (1994), 125-199.
  41. Tondo, G., On the integrability of stationary and restricted flows of the KdV hierarchy. J. Phys. A: Mat. Gen. 28 (1995), 5097-5115.
  42. Vanhaecke, P., Linearising two-dimensional integrable systems and the construction of action-angle variables. Math. Z. 211 (1992), 265-313.
  43. Vanhaecke, P., Integrable systems in the realm of algebraic geometry. Lecture Notes in Math. 1638, Springer-Verlag, 2001.
  44. van Moerbeke, P. and Mumford, D., The spectrum of difference operators and algebraic curves. Acta Math. 143 (1979), 93-154.
  45. Verhoeven, C., Musette, M. and Conte, R., General solution of hamiltonians withs extend cubic and quartic potentials. Theor. Math. Phys. 134 (2003), 128-138.
  46. Wojciechowski, S., On a Lax-type representation and separability of the anisotropic harmonic oscillator in a radial quartic potential. Lett. Nuovo Cimento, 41 (1984), 361-369.
  47. Wojciechowski, S., Integrability of one particle in a perturbed central quartic potential. Physica Scripta, 31 (1985), 433-438.
  48. Yoshida, H., Existence of exponentially unstable solutions and the non-integrability of homogeneous hamiltonian. Physica D, 21 (1986), 163-170.
  49. Zakharov, V.E., Manakov, S.V., Novikov, S.P. and Pitaevskii, L.P., Soliton theory, inverse scattering method. Moscow: Nauka, 1980.
  50. Ziglin, S.L., Branching of solutions and non-existence of first integrals in hamiltonian mechanics II. Funct. Anal. and its appl. 17 (1983), 6-17.
  51. Lesfari, A.: Algebraic integrability: the Adler-van Moerbeke approach. Regul. Chaotic Dyn. 16 (2011), Nos.3-4, pp.187-209.