\documentstyle{article}


\title{ON THE HECUBA GAP}
\author{S.FERRAZ-MELLO\\
Instituto Astron\^omico e Geof\'{\i}sico,\\ 
Universidade de S\~ao Paulo,\\ 
Caixa Postal 9638, S\~ao Paulo, SP, Brasil.}
\date{}
\begin{document}
\maketitle
Several recent results point to chaotic diffusion of the
orbits as the main mechanism in the origin of all Kirkwood gaps.
However, in the case of the 2/1 Kirkwood gap, it has not yet been
possible to have a complete identification of these mechanisms
This situation is due essentially to the fact that the time scale 
of evolutionary chaotic processes at work in this resonance are 
of the order of the age of the Solar System. 
The results presented in this communication were obtained with
Hadjidemetriou's mapping modified to use almost local expansions 
valid in high eccentricities and to take into account the main 
perturbations of Jupiter's orbit. This mapping allows simulations 
over 1 Gyr in short calculation times, 
In order to accelerate the diffusion processes the models were scaled.
The scaling is done by means of a mass gauge introduced
into the equations in such a way that all frequencies are almost 
equally scaled so that the resonant structure of the averaged system
is not altered.
The results points to the diffusion to high eccentricities of all 
orbits starting in the middle of the resonance, even when only a planar 
model is considered. They also show that a decisive role is played by 
the perturbations in Jupiter's orbit associated with the angles 
$\lambda_{Jup}-2\lambda_{Sat}$ and $2\lambda_{Jup}-5\lambda_{Sat}$.


\end{document}
