Invariant metric for nonlinear symplectic maps

Abstract

In this paper, we construct an invariant metric in the space of homogeneous polynomials of a given degree ( greater than or equal to 3). The homogeneous polynomials specify a nonlinear symplectic map which in turn represents a Hamiltonian system. By minimizing the norm constructed out of this metric as a function of system parameters, we demonstrate that the performance of a nonlinear Hamiltonian system is enhanced.