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Nonintegrability Detected from Geometrically Similar Orbits

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Abstract

H. Yoshida’s criterion of nonintegrability is restated in the light of the inverse problem of dynamics. It is shown that, given a monoparametric family of geometrically similar orbits, one may be able to assert nonintegrability of all or some homogeneous potentials of integer degreem (≠ 0, ± 2)which can produce this family.

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References

  1. Bozis, G.: 1995, Inverse Problems 11, 6

    Article  MATH  MathSciNet  ADS  Google Scholar 

  2. Bozis, G. and Stefiades, A.: 1993, Inverse Problems 9, 233

    Article  MATH  MathSciNet  ADS  Google Scholar 

  3. Hietarinta, J.: 1987, Phys. Rep. 147, 87.

    Article  MathSciNet  ADS  Google Scholar 

  4. Kozlov, V. V.: 1983, Russian Math. Surveys 38, 1.

    Article  MATH  Google Scholar 

  5. Melnikov, V. K.: 1963, Trans. Moscow Math. Soc. 12, 1.

    MATH  Google Scholar 

  6. Moser, J.: 1973, 'Stable and Random Motions in Dynamical Systems', Princeton Univ. Press, Princeton.

  7. Poincaré, H.: 1892, 'Les Méthodes Nouvelles de la Mécanique Céleste', Vol. I, Gauthier-Villards, Paris; English translation. D. L. Gorroff (ed.) 1993, 'New Methods in Celestial Mechanics', American Inst. of Physics.

  8. Smale, S.: 1963, in S. S. Cairns (ed.), 'Differential and Combinatorial Topology', Princeton Univ. Press, Princeton, p. 63.

  9. Whittaker, E. T.: 1944, 'A Treatise of the Analytical Dynamics of Particles and Rigid Bodies', Cambridge Univ. Press, Cambridge.

  10. Wiggins S.: 1990, 'Introduction to Applied Nonlinear Dynamical Systems and Chaos', Springer-Verlag, New York.

    Google Scholar 

  11. Yoshida, H.: 1987, Physica D 29, 128.

    Article  MATH  MathSciNet  ADS  Google Scholar 

  12. Yoshida, H.: 1988, Commun. Math. Phys. 116, 529.

    Article  MATH  ADS  Google Scholar 

  13. Ziglin, S. L.: 1983, Func. Anal. Appl. 16, 181; 17, 6.

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Physics, University of Thessaloniki, 54006, Greece

    G. Bozis & E. Meletlidou

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  1. G. Bozis
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  2. E. Meletlidou
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Bozis, G., Meletlidou, E. Nonintegrability Detected from Geometrically Similar Orbits. Celestial Mechanics and Dynamical Astronomy 68, 335–346 (1997). https://doi.org/10.1023/A:1008248706829

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  • DOI: https://doi.org/10.1023/A:1008248706829

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