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Keywords:

  • chaos;
  • instabilities;
  • methods: analytical

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.