Mei symmetries and conserved quantities for non-conservative Hamiltonian difference systems with irregular lattices

Abstract

Noether conserved quantities and Mei sym- metries for non-conservative Hamiltonian difference systems with irregular lattices are studied. The gener- alized Hamiltonian equations of the systems are given on the basis of the transformation operators in the space of discrete Hamiltonians. The Lie point transfor- mations acting on the lattice, as well as the difference equations, and the determining equations of Mei sym- metries are obtained for the systems. The discrete ver- sions of Noether conserved quantity are constructed by the Mei symmetries. An example is presented to illustrate the results.