Copyright © 2009 Weihong Huang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
A general formulation for multi-branches complete chaotic maps that preserve a specified invariant density is provided and an implication relationship among this class of maps is revealed. Such relationship
helps to derive a whole family of complete chaotic maps that preserve not only the same invariant measure
but also the same degree of chaos in terms of Lyapunov component.