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Analytical relation between two chaos indicators: FLI and MEGNO

Authors

  • M. F. Mestre,

    Corresponding author
    1. Grupo de Caos en Sistemas Hamiltonianos, Facultad de Ciencias Astronómicas y Geofísicas, Universidad Nacional de La Plata, Instituto de Astrofísica de La Plata (CCT La Plata – CONICET, UNLP), Paseo del Bosque s/n, 1900 La Plata, Argentina
      E-mail: mmestre@fcaglp.unlp.edu.ar (MFM); pmc@fcaglp.unlp.edu.ar (PMC); giordano@fcaglp.unlp.edu.ar (CMG)
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  • P. M. Cincotta,

    Corresponding author
    1. Grupo de Caos en Sistemas Hamiltonianos, Facultad de Ciencias Astronómicas y Geofísicas, Universidad Nacional de La Plata, Instituto de Astrofísica de La Plata (CCT La Plata – CONICET, UNLP), Paseo del Bosque s/n, 1900 La Plata, Argentina
      E-mail: mmestre@fcaglp.unlp.edu.ar (MFM); pmc@fcaglp.unlp.edu.ar (PMC); giordano@fcaglp.unlp.edu.ar (CMG)
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  • C. M. Giordano

    Corresponding author
    1. Grupo de Caos en Sistemas Hamiltonianos, Facultad de Ciencias Astronómicas y Geofísicas, Universidad Nacional de La Plata, Instituto de Astrofísica de La Plata (CCT La Plata – CONICET, UNLP), Paseo del Bosque s/n, 1900 La Plata, Argentina
      E-mail: mmestre@fcaglp.unlp.edu.ar (MFM); pmc@fcaglp.unlp.edu.ar (PMC); giordano@fcaglp.unlp.edu.ar (CMG)
    Search for more papers by this author

E-mail: mmestre@fcaglp.unlp.edu.ar (MFM); pmc@fcaglp.unlp.edu.ar (PMC); giordano@fcaglp.unlp.edu.ar (CMG)

ABSTRACT

We report an intrinsic relation between the mean exponential growth factor of nearby orbits (MEGNO) and the fast Lyapunov indicator (FLI), two variational methods that have been widely applied to stability issues in astronomy. For both continuous-time and discrete-time systems, we arrive at an analytic formula that expresses the MEGNO in terms of the FLI and its time-average. This connection, unknown for more than 10 years, allows us to understand the differences and similarities in the performance of both indicators.

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