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A Study of the Local Lyapunov Numbers for Orbits in the Outer Solar System

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The Dynamical Behaviour of our Planetary System
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Abstract

We present the distributions of the local Lyapunov characteristic numbers (LLCNs) of Pluto’s orbit and of some fictitious neighbouring orbits in the outer solar system, where the Sun (whose mass was increased by the masses of the inner planets) and the giant planets (Jupiter to Neptune) represent the perturbing bodies. According to a former study—where the extension of a “stable region” near Pluto’s orbit has been determined—we compared the distributions of the LLCNs of orbits inside this region with those outside. Furthermore, the study of the LLCNs of each orbit was carried out for différent time intervals.

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References

  • Contopoulos, G., Voglis, N., Efthymiopoulos, C., Grousouzakou, E.: 1995, “Invariant Spectra of Dynamical Systems”, preprint.

    Google Scholar 

  • Dvorak, R., Lohinger, E., Maindl, T.I.: 1995, “On the chaoticity of Pluto’s orbit”, Perturbation theory and chaos in nonlinear dynamics with emphasis to celestial mechanics (Hagel et al., eds.), Universidade da Madeira and University of Vienna (ISBN 3-901 617-00-0), p. 20–29.

    Google Scholar 

  • Dvorak, R., Lohinger, E.: 1996, “Pluto’s Lyapunov numbers in different dynamical models”, Proceedings of the IAU Symposium No. 172, in press.

    Google Scholar 

  • Froeschlé, C., Froeschlé, Ch., Lohinger, E.: 1993, “Generalized Lyapunov Characteristic Indicators and corresponding Kolmogorov like Entropy of the Standard Mapping”, Celest. Mech., 56, p. 307–314.

    Article  ADS  MATH  Google Scholar 

  • Froeschlé, C.: 1995, private communication

    Google Scholar 

  • Gonczi, R.: 1995, private communication

    Google Scholar 

  • Lohinger, E., Froeschlé, C., Dvorak, R.: 1993, “Generalized Lyapunov Exponents Indicators in Hamiltonian Dynamics: an Application to a Double Star System”, Celest. Mech., 56, p. 315–322.

    Article  ADS  MATH  Google Scholar 

  • Smith, H., Contopoulos, G.: 1995, “Spectra and Lyapunov Numbers in Pulsating Systems.”, preprint.

    Google Scholar 

  • Sussman, G.J., Wisdom, J.: 1988, “Numerical Evidence that the Motion of Pluto is chaotic”, Science, 241, p. 433–437.

    Article  ADS  Google Scholar 

  • Sussman, G.J., Wisdom, J.: 1992, “Chaotic Evolution of the Solar System”, Science, 257, p. 56–62.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Voglis, N., Contopoulos, G.: 1994, “Invariant spectra of orbits in dynamical system”, J. Phys. A, 27, p. 4899–4909.

    Article  MathSciNet  ADS  MATH  Google Scholar 

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© 1997 Springer Science+Business Media Dordrecht

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Lohinger, E. (1997). A Study of the Local Lyapunov Numbers for Orbits in the Outer Solar System. In: Dvorak, R., Henrard, J. (eds) The Dynamical Behaviour of our Planetary System. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5510-6_28

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  • DOI: https://doi.org/10.1007/978-94-011-5510-6_28

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-6320-3

  • Online ISBN: 978-94-011-5510-6

  • eBook Packages: Springer Book Archive

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