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5. Conclusions

Among the applications of this algorithm, which are the goals of our future work, we can list the following ones:

Secular resonances: to find the location of the main resonances in the phase space; this requires to compute the proper frequencies on some regularly spaced grid.

Proper elements: these could be computed for planet-crossing objects too. This would allow the identification of meteor streams and the search for their parent bodies.

Encounter conditions: by computing the mean orbital elements at the different node crossings, the radians, date and velocity (see Valsecchi et al. 1998) can be derived; this would allow us to identify the different encounters with the same meteor stream.

The collision probability with a planet is also a function of the encounter conditions and of the qualitative behaviour of the average orbit (see Gronchi and Milani 1999).

G.-F. Gronchi