What is the Hamiltonian of this number theoretic system?
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In mechanics, a Hamiltonian system describes a motion involving holonomic constraints and forces which have a potential (cf. Hamilton equations). Many problems in theoretical physics also lead to a Hamiltonian system or else to partial differential equations with similar properties, which may be treated as infinite-dimensional analogues of Hamiltonian systems.
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Hamiltonian system is a dynamical systemgoverned by Hamilton's equations. In physics, this dynamical system describes the evolution of a physical system such as a planetary system or an electron in an electromagnetic field. These systems can be studied in both Hamiltonian mechanics and dynamical systems theory.
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