The Real Period Function of A3 Singularity and Perturbations of the Spherical Pendulum

Compositio Mathematica

Volumn 123, Issue 2, 2000, Pages 167-184

  Gavrilov, Lubomir ^a   Vivolo, Olivier ^a  

^a INSTITUT DE MATHÉMATIQUES DE TOULOUSE   (France)

Author keywords

Elliptic integral; KAM theory; Spherical pendulum

Indexed keywords

EID: 0003206189     PISSN: 0010437X     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1001821300769     Document Type: Article

References (15)

1. Arnold, V. I.: Geometrical Methods in the Theory of Ordinary Differential Equations, Springer, New York, 1988.
2. Arnold, V. I.: Mathematical Methods of Classical Mechanics, Springer, New York, 1978.
3. Arnold, V. I., Gusein-Zade, S. M. and Varchenko, A. N.: Singularities of Differentiable Maps, I and II, Birkhäuser, Basel, 1988.
4. Arnold, V. I. and Il'yashenko, Yu. S.: Ordinary differential equations, In: Dynamical Systems I, Encyclopaedia of Math. Sci. 1, Springer, Berlin, 1988.
5. Audin, M.: Spinning Tops, Cambridge Stud. Adv. Math. 51, Cambridge Univ. Press, 1996.
6. Cushman, R. and Bates, L.: Global Aspects of Classical Integrable Systems, Birkhäuser, Basel, 1997.
7. Erdély, A. (ed.): Bateman Manuscript Project, Higher Transcendental Functions, vol. II, McGraw-Hill, Englewood Cliffs, 1953.
8. Duistermaat, J. J.: On global action-angles coordinates, Comm. Pure Appl. Math. 32, (1980), 687-706.
9. Gavrilov, L.: Petrov modules and zeros of Abelian integrals, Bull. Sci. Math. 122 (1998) 571-584.
10. Horozov, E.: Perturbations of the spherical pendulum and Abelian integrals, J. Reine Angew. Math. 408 (1990) 114-135
11. Il'yashenko, Yu. and Yakovenko, S. (eds.): Concerning Hilbert's 16th Problem, Adv. in Math. Sci. 27, Amer. Math. Soc., Providence, 1995.
12. Petrov, G. S.: Number of zeros of complete Abelian integrals, Funct. Anal. Appl. 18 (1984), 73-74.
13. Vivolo, O.: The monodromy of action variables of Lagrange top, Preprint 62, Laboratoire Emile Picard, University of Toulouse III, 1995, to appear in J. Geom. Physics.
14. Whittaker, E. T.: A Treatise on the Analytical Dynamics of Particles and Bodies, Cambridge Univ. Press, 1904.
15. Weil, A.: Remarques sur un mémoire d'Hermite, Collected Papers, 2, pp. 111-116.