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 Limit Point, Strong Limit Point and Dirichlet Conditions for Discrete Hamiltonian Systems Zhaowen Zheng,Jing Shao Keywords:Discrete Hamiltonian system, linear relation, limit point case, strong limit point case,Dirichlet condition. Abstract: This paper deals with discrete Hamiltonian systems with a singular endpoint. The limit point condition, the strong limit point condition and the Dirichlet condition are studied based on asymptotic behaviors or square summabilities in the maximal domains. The equivalence between the limit point and strong limit point conditions is established for a class of such systems; and for degenerated Hamiltonian system, the three conditions are shown to imply each other.