Incomplete information and fractal phase space

The incomplete statistics for complex systems is characterized by a so called incompleteness parameter omega which equals unity when information is completely accessible to our treatment. This paper is devoted to the discussion of the incompleteness of accessible information and of the physical signification of omega on the basis of fractal phase space. omega is shown to be proportional to the fractal dimension of the phase space and can be linked to the phase volume expansion and information growth during the scale refining process. (C) 2003 Elsevier Ltd. All rights reserved.