ABSTRACT
This chapter introduces an incredibly helpful tool for describing and cataloging the global dynamics of some dynamical systems that exhibit dynamics that initially seem beyond description. This tool boils down to describing orbits with infinite sequences of zero's and one's. And these sequences are pretty straightforward to understand. The chapter describes the fate of every possible initial condition in R. The best way to fully understand and appreciate the dynamics of the doubling map is to represent the numbers in the unit interval in binary. The ability to work with geometric series is extremely important in understanding the complicated dynamics.
