Decomposing a new nonlinear differentialdifference system under a Bargmann implicit symmetry constraint 
Xinyue Li,QiuLan Zhao 
Keywords:Integrable lattice equations, Symplectic map, Implicit symmetry constraint, Finitedimensional Hamiltonian system. 
Abstract: 
Firstly, a hierarchy of integrable lattice equations
and its biHamiltonian structures are established by applying the discrete trace identity. Secondly, under an implicit Bargmann
symmetry constraint, every lattice equation in the nonlinear differentialdifference system is decomposed by an completely integrable symplectic map and a finitedimensional Hamiltonian system. Finally, the
spatial part and the temporal part of the Lax pairs and adjoint Lax
pairs are all constrained as finite dimensional Liouville integrable Hamiltonian systems. 



