Exploded Points

Abstract

A new concept of a mathematical object of zero dimension, an exploded point, is introduced. The dimension used is defined on the basis of the functional characteristics of the system, thus it may be referred to as f-dimension. A stability index is also defined for the mathematical objects including exploded points, which can be related to the f-dimension. It is shown that the mathematical object exhibited by the Lorenz system after the second bifurcation is such a point. A recursive formula based on the definition of the exploded point. © 1981, Walter de Gruyter. All rights reserved.