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Ablowitz, M.J., Ramani, A., Segur, H.: Nonlinear evolution equations and ordinary differential equations of Painléve type. Nuovo Cim.23, 333–338 (1978)
Adler, M., van Moerbeke, P.: The algebraic integrability of geodesic flow on (SO(4). Invent. Math.67, 297–326 (1982), with an appendix by D. Mumford
Adler, M., van Moerbeke, P.: Kowalewski's Asymptotic Method, Kac-Moody Lie Algebras and Regularization, Commun. Math. Phys.83, 83–106 (1982)
Adler, M., van Moerbeke, P.: Geodesic flow onSO(4) and the intersection of quadrics. Proc. Nat'l. Acad. Sci. USA81, 4613–4616 (1984)
Adler, M., van Moerbeke, P. A systematic approach towards solving integrable systems, preprint 1985, to appear in revised form in (Perspective in Mathematics). New York: Academic Press 1989
Arnold, V.I.: Mathematical methods of classical mechanics. Berlin-Heidelberg-New York: Springer 1978
Bountis, T.: A singularity analysis of integrability and chaos in dynamical systems. In: Singularities and Dynamical Systems. Proceedings, Heraklion, Greece, North-Holland-Amsterdam 1983.
Ercolani, N., Siggia, E.: Painlevé property and geometry. Preprint, (Dec. 1987)
Flaschka, H.: The Toda lattice in the complex domain. Preprint, (Dec. 1987)
Dorrizzi, B., Grammaticos, B., Ramani, A.: A New Class of Integrable Systems. J. Math. Phys.24, 2282–2288 (1983)
Griffiths, P., Harris, J.: Principles of algebraic geometry. New York: Wiley Interscience 1978
Haine, L.: The Algebraic integrability of geodesic flow onSO(n). Comm. Math. Phys.94, 271–287 (1984)
Hietarinta, J.: Direct methods for the Search of the second invariant. Phys. Rep.147(2), (March 1987), North-Holland-Amsterdam
Koizumi, S.: Theta relations and projective normality of Abelian varieties. Am. J. Math.98, 865–889 (1976)
Kowalewski, S.: Sur le problème de la rotation d'un corps solid autour d'un pointe fixe. Acta Math.12, 177–232 (1889)
Kruskal, M., Clarkson, P.: The Painlevé and Poly-Painlevé tests for integrability. P. Winternitz ed., Presses Univ. de Montréal. Montreal Lectures Notes, (Aug. 1985)
Moishezon, B.G.: Onn-dimensional compact varieties withn algebraically independent meromorphic functions. Am. Math. Soc. Transl.63, 51–177 (1967)
Siegel, C.: Topics in complex functions theory, vol. 3. Tracts in Pure and Applied Mathematics, pp. 4–12. New York: Wiley 1973
Steeb, W., Kloke, M., Spieker, B., Kunick, A.: Integrability of dynamical systems and the singular-point analysis. Found. Phys.15, (1985)
Weiss, J., Tabor, M., Carnevale, G.: The Painlevé property for partial differential equations. J. Math. Phys.24, 522–526 (1983)
Yoshida, H.: Necessary conditions for the existence of algebraic first integals, I: Kowalewski's exponents. J. Celest. Mech.31, 363–379 (1983)
Bureau, F.J.: Les systémes différentiels non-linéaires dans le champ complexe. Etude globale; essai de synthèse. Actas del V Congreso de la Agrupación de Matemáticos de Expresión Latina. 114–142 (1978)
Françoise, J.P.: Integrability of quasi-homogeneous vector fields (preprint)
Hartshorne, R.: Algebraic Geometry. Berlin-Heidelberg-New York: Springer 1977
Mumford, D.: Algebraic Geometry I. Complex Projective Varieties. Berlin-Heidelberg-New York: Springer 1976
Mumford, D.: Tata Lectures on Theta II. Boston-Basel: Birkhäuser 1984
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The support of a National Science Foundation grant #DMS-8703407 is gratefully acknowledged
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Adler, M., van Moerbeke, P. The complex geometry of the Kowalewski-Painlevé analysis. Invent Math 97, 3–51 (1989). https://doi.org/10.1007/BF01850654
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DOI: https://doi.org/10.1007/BF01850654