Hessian-information geometric formulation of Hamiltonian systems and generalized Toda's dual transform

摘要

In this paper a class of classical Hamiltonian systems is geometricallyformulated. This class is such that a Hamiltonian can be written as the sum ofa kinetic energy function and a potential energy function. In addition, theseenergy functions are assumed strictly convex. For this class of Hamiltoniansystems Hessian and information geometric formulation is given. With thisformulation, a generalized Toda's dual transform is proposed, where hisoriginal transform was used in deriving his integrable lattice system. Then arelation between the generalized Toda's dual transform and the Legendretransform of a class of potential energy functions is shown. As an extension ofthis formulation, dissipation-less electric circuit models are also discussedin the geometric viewpoint above.