Context :

Aims : We analyze the dynamics of small body reservoirs under the effects of an eccentric inner giant planet resulting from a planetary scattering event around a 0.5 M _ { \odot } star .

Methods : First , we used a semi-analytical model to define the properties of the protoplanetary disk that lead to the formation of three Jupiter-mass planets .
Then , we carried out N-body simulations assuming that the planets are close to their stability limit together with an outer planetesimal disk .
In particular , the present work focused on the analysis of N-body simulations in which a single Jupiter-mass planet survives after the dynamical instability event .

Results : Our simulations produce outer small body reservoirs with particles on prograde and retrograde orbits , and other ones whose orbital plane flips from prograde to retrograde and back again along their evolution ( “ Type-F particles ” ) .
We find strong correlations between the inclination i and the ascending node longitude \Omega of Type-F particles .
First , \Omega librates around 90 \degr or/and 270 \degr .
This property represents a necessary and sufficient condition for the flipping of an orbit .
Moreover , the libration periods of i and \Omega are equal and they are out to phase by a quarter period .
We also remark that the larger the libration amplitude of i , the larger the libration amplitude of \Omega .
We analyze the orbital parameters of Type-F particles immediately after the instability event ( post IE orbital parameters ) , when a single Jupiter-mass planet survives in the system .
Our results suggest that the orbit of a particle can flip for any value of its post IE eccentricity , although we find only two Type-F particles with post IE inclinations i \lesssim 17 \degr .
Finally , our study indicates that the minimum value of the inclination of the Type-F particles in a given system decreases with an increase in the eccentricity of the giant planet .

Conclusions :