Catalytic system based at least: • on a metallocene of formula • on an organometallic compound as cocatalyst selected from the group consisting of alkylmagnesium compounds, alkyllithium compounds, Grignard reagents and mixtures of alkyllithium compounds and alkylaluminium compounds, [{P(Cp 1)(Cp 2)MetG x} p] - Met being a rare earth metal atom, - the symbol G representing a halogen atom chosen from chlorine, iodine and bromine, or a monovalent ligand chosen from the borohydride BH 4 group, amide groups, alkyl groups and silylalkyl groups, - L representing a molecule of a complexing solvent, - x, which is or is not an integer, being greater than or equal to 0, - p, which is an integer, being equal to 1 or 2, - Cp 1 and Cp 2, which are identical or different, being selected from the group consisting of cyclopentadienyl groups substituted at least in the 2 and 5 positions, substituted fluorenyl groups, the unsubstituted fluorenyl group and indenyl groups substituted at least in the 2 position, - the substituents in the 2 and 5 positions of the cyclopentadienyl groups and the substituent in the 2 position of the indenyl groups being alkyls or aryls, - P being a group which bridges Cp 1 and Cp 2 and which corresponds to the formula MR 1 R 2, with M representing a Si or C atom and with R 1 and R 2, which are identical or different, representing an alkyl group, - with the condition that, if Cp 1 is an unsubstituted fluorenyl group, Cp 2 is other than an unsubstituted fluorenyl group, preferably other than an unsubstituted fluorenyl group and than a substituted fluorenyl group. • on a metallocene of formula • on an organometallic compound as cocatalyst selected from the group consisting of alkylmagnesium compounds, alkyllithium compounds, Grignard reagents and mixtures of alkyllithium compounds and alkylaluminium compounds, [{P(Cp 1)(Cp 2)MetG x} p] - Met being a rare earth metal atom, - the symbol G representing a halogen atom chosen from chlorine, iodine and bromine, or a monovalent ligand chosen from the borohydride BH 4 group, amide groups, alkyl groups and silylalkyl groups, - L representing a molecule of a complexing solvent, - x, which is or is not an integer, being greater than or equal to 0, - p, which is an integer, being equal to 1 or 2, - Cp 1 and Cp 2, which are identical or different, being selected from the group consisting of cyclopentadienyl groups substituted at least in the 2 and 5 positions, substituted fluorenyl groups, the unsubstituted fluorenyl group and indenyl groups substituted at least in the 2 position, - the substituents in the 2 and 5 positions of the cyclopentadienyl groups and the substituent in the 2 position of the indenyl groups being alkyls or aryls, - P being a group which bridges Cp 1 and Cp 2 and which corresponds to the formula MR 1 R 2, with M representing a Si or C atom and with R 1 and R 2, which are identical or different, representing an alkyl group, - with the condition that, if Cp 1 is an unsubstituted fluorenyl group, Cp 2 is other than an unsubstituted fluorenyl group, preferably other than an unsubstituted fluorenyl group and than a substituted fluorenyl group. - Met being a rare earth metal atom, - the symbol G representing a halogen atom chosen from chlorine, iodine and bromine, or a monovalent ligand chosen from the borohydride BH 4 group, amide groups, alkyl groups and silylalkyl groups, - L representing a molecule of a complexing solvent, - x, which is or is not an integer, being greater than or equal to 0, - p, which is an integer, being equal to 1 or 2, - Cp 1 and Cp 2, which are identical or different, being selected from the group consisting of cyclopentadienyl groups substituted at least in the 2 and 5 positions, substituted fluorenyl groups, the unsubstituted fluorenyl group and indenyl groups substituted at least in the 2 position, - the substituents in the 2 and 5 positions of the cyclopentadienyl groups and the substituent in the 2 position of the indenyl groups being alkyls or aryls, - P being a group which bridges Cp 1 and Cp 2 and which corresponds to the formula MR 1 R 2, with M representing a Si or C atom and with R 1 and R 2, which are identical or different, representing an alkyl group, - with the condition that, if Cp 1 is an unsubstituted fluorenyl group, Cp 2 is other than an unsubstituted fluorenyl group, preferably other than an unsubstituted fluorenyl group and than a substituted fluorenyl group.