GOVINDAN RANGARAJAN*+ and MINITA SACHIDANAND *

* Department of Mathematics, Indian Institute of Science, Bangalore 560 012, India

+ Also at Centre for Theoretical Studies, Indian Institute of Science, Bangalore, India

+ Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore, India
Email: rangaraj@math.iisc.ernet.in

Abstract.

In this paper, we construct an invariant metric in the space of homogeneous polynomials of a given degree ( ³3). 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.

Keywords:  Invariant metric; symplectic maps; performance optimization.

Pacs Nos.  05.45.-a; 02.20.-a; 45.20.Jj; 41.85.-p