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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.26 no.2 Antofagasta Aug. 2007

http://dx.doi.org/10.4067/S0716-09172007000200003 

Proyecciones Journal of Mathematics
Vol. 26, Nº 2, pp. 189-206, August 2007.
Universidad Católica del Norte
Antofagasta - Chile


PERIODIC SOLUTIONS IN THE SINGULAR LOGARITHMIC POTENTIAL


CLAUDIO VIDAL

Universidad del Bio Bio, Chile


Correspondencia a:



Abstract
We consider the singular logarithmic potential , a potential which plays an important role in the modelling of triaxial systems, such as elliptical galaxies or bars in the centres of galaxy discs. Using properties of the central field in the axis-symmetric case we obtain periodic solutions which are symmetric with respect to the origin for weak anisotropies. Also we generalize our result in order to include more general perturbations of the logarithmic potential.

Mathematics Subject Classification : 34C25, 34CI4.potential, symmetry.

Key words : Orlicz-Sobolev spaces, strongly nonlinear problems.

REFERENCES
[1] Arnold, V. Mathematical Methods of Classical Mechanics, Springer-Verlag, Berlin Heidelberg, New York, (1978).         [ Links ]
[2] Azevédo, C. Dinámica do problema do fio circular homogñeo, Thesis for Degree of Doctor in Mathematics, Universidade Federal de Pernambuco. Brazil, (2002).         [ Links ]
[3] Azevédo, C. and Ontaneda, P. 'Continuous symmetric perturbations of planar power law forces', J. Diff. Eq., 211, pp. 20-37, (2005).         [ Links ]
[4] Birkhoff, G. 'The restricted problem of three bodies. Rend. Circ. Mat. Palermo, 30, pp. 1-70, (1915).         [ Links ]
[5] Boccaletti, D. and Pucaco, G. Theory of orbits, Springer-Verlag, Berlin Heidelberg, New York, (1996).         [ Links ]
[6] Cabral, H. and Vidal, C. 'Periodic solutions of symmetric perturbations of the Kepler problem'. J. Diff. Eq., 163, pp. 76-88, (2000).         [ Links ]
[7] Caranicolas, N., and Barbanis, B. 'Periodic orbits in nearly axisymmet-ric stellar systems'. Astron. and Astroph., 114, pp. 360-366, (1982).         [ Links ]
[8] Caranicolas, N., and Vozikis, CH. 'Orbital characterizations of dynamical models of elliptical galaxies', Celest. Mech., 39, pp. 85-102, (1986).         [ Links ]
[9] Casasayas, J. and Llibre, J.: 'Qualitative analysis of the Anisotropic Kepler problem', Memoirs Amer. Math. Soc, 314, (1984).         [ Links ]
[10] Piccinini, L., Stampacchia, G. and Vidossich, G. Ordinary Differential Equations in Mn, Aplied Mathematical Sciences, 39, Springer-Verlag, (1978).         [ Links ]
[11] Santoprete, M. 'Symmetric periodic solutions of the anisotropic Manev problem', Journal of Mathematical Physics, 43, pp. 3207-3219, (2002).         [ Links ]
[12] Stoica, C. and Font, A. 'Global dynamics in the singular logarithmic potential', J. Phys. A: Math. Gen., 36, pp. 7693-7714, (2003).         [ Links ]
[13] Schwarzschild, M. Astrophys. J, 232, 236, (1979).         [ Links ]
[14] Vidal, C. 'Periodic solutions for any planar symmetric perturbation of the Kepler problem', Celest. Mech., 80, pp. 119-132, (2001).         [ Links ]
[15] Vidal, C: 'Periodic solutions of symmetric perturbations of Gravitational potentials, J. Dyn. Diff. Eqs., 17, 1, pp. 85-114, (2005).
        [ Links ]

Claudio Vidal
Departamento de Matemática
Facultad de Ciencias
Universidad del Bio Bio,
Casilla 5-C
Concepción
VIII-Región
Chile
e-mail : clvidal@ubiobio.cl

Received : April 2007. Accepted : July 2007


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