A new integrable symplectic map for 4-field Blaszak–Marciniak lattice equations

• Discrete zero-curvature representation from new 4-order matrix spectral problem is introduced.
• Bargmann symmetry constraint and integrable symplectic map about the 4-field lattice equation in this paper is constructed first.
• The integrable finite-dimensional systems in the Liouville sense are obtained.

Based on a new discrete 4×44×4 matrix spectral problem, a hierarchy of integrable 4-field Blaszak–Marciniak lattice equations with four potentials is constructed. Moreover, a new integrable symplectic map and its evolutive system of conserved integrals are obtained by the binary nonlinearization of spatial parts and the time parts of Lax pairs and their adjoint Lax pairs of the hierarchy.