STRANGE REPELLER INDUCED BY DYNAMICAL DISCONTINUITY

Abstract

Employing a kind of piece-wise linear map with a hole,we show that “hole-induced crisis” is a result of the emergence of a “strange repeller due to discontinuity”. The strange repeller forces the iteration orbit to escape from the original chaotic attractor.Thus the attactor suddenly expands.We have proved that the lifetime of iterations in original attractor is inversely proportional to the escaping ratio,which enables us to obtain the dependence of the mean lifetime on the control parameter analytically.