Abstract: The Lie symmetry and Noether conserved quantity of discrete difference Hamilton system are investigated. Based on the extended mechanical variational principle of discrete time, the difference dynamical equations of Hamilton system are constructed. The invariance of difference equations of discrete system under infinitesimal transformation groups is defined to be Lie symmetry and the criterion for when discrete Noether conserved quantities may be obtained from Lie symmetries is also deduced. An example is discussed to show the applications of the results.

Keywords: 
• discrete mechanics /
• difference Hamilton system /
• Lie symmetry /
• Noether conserved quantity