The current giant planet region is a transitional zone where transneptunian objects (TNOs) cross in their way to becoming Jupiter Family Comets (JFCs). Their dynamical behavior is conditioned by the intrinsic dynamical features of TNOs and also by the encounters with the giant planets. We address the Giant Planet Crossing (GPC) population (those objects with $5.2$ au $ < q < 30$ au) studying their number and their evolution from their sources, considering the current configuration of the Solar System. This subject is reviewed from previous investigations and also addressed by new numerical simulations of the dynamical evolution of Scattered Disk Objects (SDOs). We obtain a model of the intrinsic orbital element distribution of GPCs. The Scattered Disk represents the main source of prograde GPCs and Centaurs, while the contribution from Plutinos lies between one and two orders of magnitude below that from the SD. We obtain the number and size distribution of GPCs from our model, computing 9600 GPCs from the SD with $D > 100$ km and $sim 10^8$ with $D > 1$ km in the current population. The contribution from other sources is considered negligible. The mean lifetime in the Centaur zone is 7.2 Myr, while the mean lifetime of SDOs in the GPC zone is of 68 Myr. The latter is dependent on the initial inclination, being the ones with high inclinations the ones that survive the longest in the GPC zone. There is also a correlation of lifetime with perihelion distance, where greater perihelion leads to longer lifetime. The dynamical evolution of observed GPCs is different for prograde and retrograde objects. Retrograde GPCs have lower median lifetime than prograde ones, thus experiencing a comparatively faster evolution. However, it is probable that this faster evolution is due to the fact that the majority of retrograde GPCs have low perihelion values and then, lower lifetimes.
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