Abstract
In this paper, we consider analytical formulation method of an impact oscillator system which is typical piecewise linear System, from a viewpoint of integrable system. First, global representation of general solution of the target system that is preveously proposed by present author can be regarded as rigourous discretization by means of unequally spaced difference scheme in relation to impact times. This means that dynamics of the impact oscillator as continous-time dynamical system is doublly prescribed by nonlinear difference equation governing impact times transcendentally and linear diference equation with regard to time evalution between impact states. Finaly, it is shown that piecewise linear system is exact solvable chaotic generating system that is included different important category, self reference system, hybrid system, and integrable system.
