The mean semimajor axis is output from the simulation every 1000 yr, so to see the fine structures of the miniresonances.    In order to obtain a first approximation of proper elememnts we averaged the osculating elements with with a running window of 10~Myrs and a shift of 100,000 years.   We call the results of this procedure ``averaged'' elements.   We have carried out three simulations for the Adeona and Gefion families:
 

1. Current members of the family (according to Cellino's file) under the action of close encounters with Ceres, Pallas, Vesta, and Hygiea.
2. Members of  a compact synthetic family under the effects of the four largest asteroids.
3. Members of the synthetic families under Yarkovsky effect.

Moreover, we have integrated members of a compact family for the case of Dora, under the action of the four largest asteroids.   Below we report our results for each family.

In the following plots we report the time evolution of the mean semimajor axis for the three integration for the Adeona members.    Red lines indicate the position of mean motion resonances with Jupiter, green line the position of mean motion resonances with Mars, blue lines stands for three-body resonances, the black line indicate the center of the family, and the yellow lines the 3-sigma level from the center.  Integration time span ~500 Myr for the real members of Adeona, ~600 Myr for members of the synthetic family integrated with SWIFT-SKEEL, and ~900 Myr for the members of the synthetic family integrated with SWIFT-RMVSY.
 

Adeona is bounded by the 8/3 mean motion resonance with Jupiter at 2.705 AU, and by the 11/4 at 2.65 AU. David Nesvorny found a significant population of asteroids beyond the 11/4 resonance for a cutoff in the velocity at v=80m/s (see adeona.080), which is consistent with the results of the Yarkovsky integration. Conversely, close encounters are not able to significantly alter dispersion in semimajor axis of the members of the family. Variations of the standard deviation in a were less than 3% at the end of the integration for both real members and simulated initial conditions.

We integrated real members of the Gefion family for ~600 Myr, "synthetic" members with close encounters for ~500 Myr, and synthetic members with Yarkovsky for about 750 Myr. Gefion is crossed by the 18/7 and 23/9 mean motion resonances with Jupiter, and is close to the 5/2 at 2.82 AU (only one particle in the Yarkovsky simulation entered this resonance), and the 13/5 at 2.7509 AU.
 
 

Gefion is the family which is closest in the orbital element space to 1 Ceres, most of its members have similar values of inclination and very high values of collision probabilities.   We believed that this family should be the most affected by close encounters with Ceres and indeed this is what we observe: while the standard deviation in a for the real members changed by 3.3% at the end of the integration, there was a change of ~30% for the case of simulated initial conditions. Most of the change occurred in the first 400 Myr of the integration, and then the dispersion in a remained approximately constant.

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