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THE FORM INVARIANCE AND THE LIE SYMMETRY OF THE GENERALIZED HAMILTONIAN SYSTEM ARE STUDIED. FIRSTLY, DE?NITIONS AND CRITERIA OF THE FORM INVARIANCE AND THE LIE SYMMETRY OF THE SYSTEM ARE GIVEN. NEXT, THE RELATION BETWEEN THE FORM INVARIANCE AND THE LIE SYMMETRY IS STUDIED. FINALLY, TWO EXAMPLES ARE GIVEN TO ILLUSTRATE THE APPLICATION OF THE RESULTS.“,”The form invariance and the Lie symmetry of the generalized Hamiltonian system are studied. Firstly, de?nitions and criteria of the form invariance and the Lie symmetry of the system are given. Next, the relation between the form invariance and the Lie symmetry is studied. Finally, two examples are given to illustrate the application of the results.