ABSTRACT
This chapter presents an investigation of orbits of discrete one-dimensional dynamical systems, particularly properties of stability and periodicity. A one-dimensional system has only a single state variable, however some have more than one parameter. The function f must have the property that the domain space is mapped to itself, so as to allow for iteration; for this reason functions determine the behaviour of dynamical systems as maps rather than functions. The chapter shows that different models often have identical patterns of behaviour which come from simple properties of the function. For this reason, it presents two special one-dimensional examples in much detail, knowing that there are general lessons to be learned. The chapter considers the one-dimensional maps available in the Graphical Analysis window of Chaos for Java, at the maximum allowed values of their parameter. Which check that there is no such coincidence for the Sine map and Tent map.
