Is the Dimension of Chaotic Attractors Invariant under Coordinate Changes?

Several different dimension-like quantities, which have been suggested as being relevant to the study of chaotic attractors, are examined. In particular, we discuss whether these quantities are invariant under changes of variables that are differentiable except at a finite number of points. It is found that some are and some are not. It is suggested that the word “dimension” be reversed only for those quantities have this invariance property.