Lie Algebraic Approach and Complex Invariant Coupled Oscillator Systems

Abstract

In classical mechanics, the system of coupled harmonic oscillators is shown to possess the symmetry applicable toa six-dimensional space in complex coordinates, twodimensional phase space consisting of two position and twomomentum variables. In search into the features of a dynamical system, with the possibility of its complex invariant,we explore this dynamical systems. Dynamical algebraic approach is used to study two-dimensional complex systems(coupled oscillator system) on the extended complex phase plane (ECPS). Scope and importance of invariants in theanalysis of complex trajectories for dynamical systems is discussed.