Catalytic system based at least: on a metallocene of formula (Ia) or (Ib), on an organomagnesium reagent as co-catalyst, {P(Cp 1)(Cp 2)Y} (Ia) Cp 3 Cp 4 Y (Ib) Y denoting a group including a rare-earth metal atom, Cp 1, Cp 2, Cp 3 and Cp 4, which are 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 organomagnesium reagent being a compound of formula R B -(Mg-R A) m -Mg-R B R B being different from R A, R B comprising a benzene nucleus substituted with the 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 a divalent aliphatic hydrocarbon-based chain, interrupted or not with one or more oxygen or sulfur atoms or with one or more arylene groups, m being a number greater than or equal to 1 and preferably equal to 1. on a metallocene of formula (Ia) or (Ib), on an organomagnesium reagent as co-catalyst, {P(Cp 1)(Cp 2)Y} (Ia) Cp 3 Cp 4 Y (Ib) Y denoting a group including a rare-earth metal atom, Cp 1, Cp 2, Cp 3 and Cp 4, which are 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 organomagnesium reagent being a compound of formula R B -(Mg-R A) m -Mg-R B R B being different from R A, R B comprising a benzene nucleus substituted with the 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 a divalent aliphatic hydrocarbon-based chain, interrupted or not with one or more oxygen or sulfur atoms or with one or more arylene groups, m being a number greater than or equal to 1 and preferably equal to 1. Y denoting a group including a rare-earth metal atom, Cp 1, Cp 2, Cp 3 and Cp 4, which are 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 organomagnesium reagent being a compound of formula R B -(Mg-R A) m -Mg-R B R B being different from R A, R B comprising a benzene nucleus substituted with the 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 a divalent aliphatic hydrocarbon-based chain, interrupted or not with one or more oxygen or sulfur atoms or with one or more arylene groups, m being a number greater than or equal to 1 and preferably equal to 1. R B being different from R A, R B comprising a benzene nucleus substituted with the 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 a divalent aliphatic hydrocarbon-based chain, interrupted or not with one or more oxygen or sulfur atoms or with one or more arylene groups, m being a number greater than or equal to 1 and preferably equal to 1.