Abstract
This chapter discusses the existence of solutions to Hamiltonian dynamical systems of optimal growth. Cass and Shell have shown how a wide range of problems in the theory of economic dynamics may be formulated in terms of Hamiltonian dynamical systems. In particular, they have studied the system modeling consumption-optimal growth with discount rate p>0. The Hamiltonian function H(Q,k) is defined on the basis of certain assumptions about technology. It presents a set of conditions on the Hamiltonian function H(Q,k) that are sufficient to guarantee that the system has a non-negative solution. These conditions include convexity-concavity and other properties that are consistent with or mimic the technological assumptions of Cass and Shell.
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