| In the study of interval dynamics exact computations are difficult, if not impossible to obtain. In practice, one uses a computer to simulate a dynamical system without regard to the accuracy of the simulation. It is known that there are dynamical systems that are very poorly behaved under any deviation from exact computation. In these cases it is of little worth to perform computer simulations on the dynamical system since the result of the simulation does not correspond to the properties of the dynamical system under study.;In this dissertation, a two parameter family of continuous transformations of an interval were examined, the Trapezoidal Maps. It was shown that not all trapezoidal maps require exact calculations to study their dynamic properties. The property of a transformation which gives rigorous meaning to non-exact computation of orbits of dynamical systems is known as the 'Shadowing Property'. The main results obtained are a classification of the entire class of trapezoidal maps by whether they possess this 'Shadowing Property' or not. |
