Catalytic system based at least: - on a metallocene of formula (la) or (Ib), preferably (la), on a diorganomagnesium compound as co-catalyst, {P(Cp 1)(Cp 2)Y} (Ia) Cp 3 Cp 4 Y (Ib) Y denoting a group including a metal atom which is a rare-earth metal, Cp 1, Cp 2, Cp 3 and Cp 4, which may be identical or different, being chosen from the group consisting of fluorenyl groups, cyclopentadienyl groups and indenyl groups, the groups being substituted or unsubstituted, P being a group bridging the two groups Cp 1 and Cp 2 and comprising a silicon or carbon atom, the diorganomagnesium compound being an asymmetric compound of formula R B -Mg-R A R B being different from R A, R B comprising a benzene nucleus substituted with a magnesium atom, one of the carbon atoms of the benzene nucleus ortho to the magnesium being substituted with a methyl, an ethyl, an isopropyl or forming a ring with the carbon atom which is its closest neighbour and which is meta to the magnesium, the other carbon atom of the benzene nucleus ortho to the magnesium being substituted with a methyl, an ethyl or an isopropyl, R A being an alkyl, a cycloalkyl or a benzyl that is substituted or not. - on a metallocene of formula (la) or (Ib), preferably (la), on a diorganomagnesium compound as co-catalyst, {P(Cp 1)(Cp 2)Y} (Ia) Cp 3 Cp 4 Y (Ib) Y denoting a group including a metal atom which is a rare-earth metal, Cp 1, Cp 2, Cp 3 and Cp 4, which may be identical or different, being chosen from the group consisting of fluorenyl groups, cyclopentadienyl groups and indenyl groups, the groups being substituted or unsubstituted, P being a group bridging the two groups Cp 1 and Cp 2 and comprising a silicon or carbon atom, the diorganomagnesium compound being an asymmetric compound of formula R B -Mg-R A R B being different from R A, R B comprising a benzene nucleus substituted with a magnesium atom, one of the carbon atoms of the benzene nucleus ortho to the magnesium being substituted with a methyl, an ethyl, an isopropyl or forming a ring with the carbon atom which is its closest neighbour and which is meta to the magnesium, the other carbon atom of the benzene nucleus ortho to the magnesium being substituted with a methyl, an ethyl or an isopropyl, R A being an alkyl, a cycloalkyl or a benzyl that is substituted or not. on a diorganomagnesium compound as co-catalyst, {P(Cp 1)(Cp 2)Y} (Ia) Cp 3 Cp 4 Y (Ib) Y denoting a group including a metal atom which is a rare-earth metal, Cp 1, Cp 2, Cp 3 and Cp 4, which may be identical or different, being chosen from the group consisting of fluorenyl groups, cyclopentadienyl groups and indenyl groups, the groups being substituted or unsubstituted, P being a group bridging the two groups Cp 1 and Cp 2 and comprising a silicon or carbon atom, the diorganomagnesium compound being an asymmetric compound of formula R B -Mg-R A R B being different from R A, R B comprising a benzene nucleus substituted with a magnesium atom, one of the carbon atoms of the benzene nucleus ortho to the magnesium being substituted with a methyl, an ethyl, an isopropyl or forming a ring with the carbon atom which is its closest neighbour and which is meta to the magnesium, the other carbon atom of the benzene nucleus ortho to the magnesium being substituted with a methyl, an ethyl or an isopropyl, R A being an alkyl, a cycloalkyl or a benzyl that is substituted or not.