Abstract
The conjecture of Poincaré (1892) on the ‘density’ of periodic orbits of the restricted 3-body problem is discussed and generalized for dynamical system with stable closed solutions. It is shown that under certain conditions the above conjecture is valid for certain domains of the phase space. Under the same conditions the ‘branching’ of a family of periodic orbits is shown to be ‘dense’.
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References
Birkhoff, B.: 1927, Dynamical Systems, Vol. 9, American Mathematical Soc., Colloquium Publ. New York.
Poincaré, H.: 1892, Les Méthodes Nouvelles de la Méchanique Céleste, Vol. 1, Dover Publ., 1957.
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© 1973 D. Reidel Publishing Company, Dordrecht-Holland
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Katsiaris, G., Goudas, C.L. (1973). On a Conjecture by Poincaré. In: Tapley, B.D., Szebehely, V. (eds) Recent Advances in Dynamical Astronomy. Astrophysics and Space Science Library, vol 39. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-2611-6_11
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DOI: https://doi.org/10.1007/978-94-010-2611-6_11
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-2613-0
Online ISBN: 978-94-010-2611-6
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